result.json

[
  {
    "title": "Simple Harmonic Motion: Crash Course Physics #16",
    "description": "Bridges... bridges, bridges, bridges. We talk a lot about bridges in physics. Why? Because there is A LOT of practical physics that ...",
    "thumbnail": "https://i.ytimg.com/vi/jxstE6A_CYQ/default.jpg",
    "videoId": "jxstE6A_CYQ",
    "transcript": "[{'text': 'In June 2001, officials in London unveiled a striking new feat of engineering: the Millennium Bridge', 'start': 3.1, 'duration': 6.16}, {'text': '-- a pedestrian bridge spanning the\\nRiver Thames.', 'start': 9.26, 'duration': 2.46}, {'text': 'It promised to be very useful, and it was\\ncool to look at, but it had to be close almost immediately.', 'start': 11.72, 'duration': 5.08}, {'text': 'Because when people used the bridge, it swayed back and forth dramatically, due to the force of their footsteps.', 'start': 16.81, 'duration': 4.67}, {'text': 'Undeterred, people kept using the bridge, but as they walked they began leaning into the swaying to keep themselves from falling over.', 'start': 21.48, 'duration': 6.54}, {'text': 'And that only made things worse.', 'start': 28.02, 'duration': 1.7}, {'text': 'Eventually, the motion of the bridge became so severe, that the bridge took on the shape of a giant S.', 'start': 29.72, 'duration': 4.82}, {'text': 'Essentially, a horizontal wave.', 'start': 34.54, 'duration': 1.66}, {'text': 'The bridge had to be closed and the engineers took nearly two years to fix it the problem.', 'start': 36.2, 'duration': 4.08}, {'text': 'So, what was wrong with the Millennium Bridge?', 'start': 40.28, 'duration': 2.28}, {'text': 'And why didn\u2019t the engineers foresee the\\nproblem?', 'start': 42.56, 'duration': 2.02}, {'text': 'The answer lies in oscillations.', 'start': 44.58, 'duration': 1.94}, {'text': '[Theme Music]', 'start': 46.52, 'duration': 12.9}, {'text': 'The physics that caused the swaying of the Millennium Bridge has to do with oscillations, or back-and-forth motion.', 'start': 59.42, 'duration': 5.08}, {'text': 'More specifically, it has to do with simple\\nharmonic motion:', 'start': 64.5, 'duration': 3.12}, {'text': 'where oscillations follow a particular, consistent pattern.', 'start': 67.62, 'duration': 3.2}, {'text': 'But before we had the Millennium Bridge as\\na real-life example,', 'start': 70.83, 'duration': 2.96}, {'text': 'physicists often described simple harmonic motion in terms of a ball attached to a horizontal spring, lying on a table.', 'start': 73.79, 'duration': 6.3}, {'text': 'While it\u2019s lying there, at rest, it\u2019s\\nin equilibrium.', 'start': 80.09, 'duration': 3.14}, {'text': 'And when you move the ball so that it stretches\\nthe spring, then let go,', 'start': 83.23, 'duration': 3.0}, {'text': 'the ball keeps moving back and forth forever...\\nin a frictionless world.', 'start': 86.23, 'duration': 4.2}, {'text': 'That back-and-forth motion caused by the force\\nof the spring, is simple harmonic motion.', 'start': 90.43, 'duration': 4.01}, {'text': 'Now, we want to know two things about this\\noscillating ball:', 'start': 94.45, 'duration': 3.09}, {'text': 'What kinds of energy does it have?', 'start': 97.54, 'duration': 1.86}, {'text': 'And, what\u2019s its maximum velocity?', 'start': 99.4, 'duration': 1.93}, {'text': 'To better understand what\u2019s happening to\\nthe ball, let\u2019s start with its energy.', 'start': 101.33, 'duration': 3.19}, {'text': 'As the ball compresses and stretches the spring, both \u2018kinetic energy\u2019 and \u2018potential energy\u2019 come into play.', 'start': 104.52, 'duration': 5.34}, {'text': 'Kinetic energy is the energy of motion, and\\nas the ball moves, there are two points --', 'start': 109.86, 'duration': 4.26}, {'text': 'the turning points -- where it\u2019s NOT moving:', 'start': 114.12, 'duration': 2.1}, {'text': 'One point is where the spring is compressed all the way, and the other is where it\u2019s stretched all the way.', 'start': 116.22, 'duration': 4.52}, {'text': 'And the distance between either of these two points, and the equilibrium point, is called the \u2018amplitude\u2019.', 'start': 120.74, 'duration': 5.18}, {'text': \"At those two turning points, the ball won\u2019t\\nhave any kinetic energy, since it isn't moving.\", 'start': 125.92, 'duration': 4.68}, {'text': 'Instead, all of the ball\u2019s energy will be\\npotential energy from the spring:', 'start': 130.6, 'duration': 3.82}, {'text': '(half of the spring constant), times the (amplitude\\nsquared).', 'start': 134.42, 'duration': 3.54}, {'text': 'Now, as the ball moves toward the middle,\\nits kinetic energy starts to increase,', 'start': 137.96, 'duration': 3.58}, {'text': 'because it\u2019s moving faster and faster.', 'start': 141.54, 'duration': 2.1}, {'text': 'And at the same time, its potential energy\\ndecreases, keeping its total energy the same.', 'start': 143.65, 'duration': 4.38}, {'text': 'And exactly in the middle of the ball\u2019s motion -- at the equilibrium point -- its potential energy goes down to 0.', 'start': 148.03, 'duration': 5.49}, {'text': 'The ball is back where it started, so the spring isn\u2019t pulling on it anymore.', 'start': 153.52, 'duration': 3.66}, {'text': 'Its kinetic energy, on the other hand, has\\nreached its maximum.', 'start': 157.18, 'duration': 2.899}, {'text': 'Which means that at that point, the total\\nenergy of the ball will be equal to', 'start': 160.079, 'duration': 3.32}, {'text': '(half of its mass), times its (maximum velocity\\nsquared).', 'start': 163.4, 'duration': 3.14}, {'text': 'Now we have two equations for the total energy in this oscillating spring, which we can combine into one equation.', 'start': 166.54, 'duration': 5.92}, {'text': 'And if we use algebra to move around its variables, we can start to answer the second question we had about the ball.', 'start': 172.46, 'duration': 5.08}, {'text': 'We wanted to know the ball\u2019s maximum velocity,\\nand this equation tells us, that it\u2019s equal', 'start': 177.54, 'duration': 4.679}, {'text': 'to the (amplitude), times the (square root\\nof the spring constant) (divided by its mass).', 'start': 182.219, 'duration': 4.41}, {'text': 'So we\u2019ve answered our two questions\\nabout the ball on the spring!', 'start': 186.629, 'duration': 2.94}, {'text': 'We know about its energy, and we have an equation for its maximum velocity.', 'start': 189.569, 'duration': 3.331}, {'text': 'But there\u2019s a lot more going on with this\\nball than just its energy and velocity.', 'start': 192.909, 'duration': 3.74}, {'text': 'It also has properties like a period,\\na frequency, and an angular velocity.', 'start': 196.649, 'duration': 4.58}, {'text': 'Plus, its position changes with time.', 'start': 201.229, 'duration': 2.031}, {'text': 'You might recognize those terms, because we\u2019ve already talked about them in our episode on uniform circular motion.', 'start': 203.26, 'duration': 4.74}, {'text': 'And that\u2019s no coincidence!', 'start': 208.0, 'duration': 1.4}, {'text': 'Simple harmonic motion is actually a lot like uniform circular motion, mathematically speaking.', 'start': 209.409, 'duration': 4.511}, {'text': 'You can see this for yourself, if you compare the ball\u2019s motion on the spring to an object in uniform circular motion --', 'start': 213.92, 'duration': 5.52}, {'text': 'say, a marble moving along a ring at a constant speed.', 'start': 219.44, 'duration': 3.32}, {'text': 'OK, I admit: It might seem like kind of a weird\\ncomparison at first.', 'start': 222.76, 'duration': 3.86}, {'text': 'For one thing, the ball on the spring is\\nmoving in one dimension,', 'start': 226.62, 'duration': 3.0}, {'text': 'while a marble moving along a circular path is in two dimensions.', 'start': 229.62, 'duration': 3.12}, {'text': 'But what if you take that ring, and look at\\nit from the side?', 'start': 232.74, 'duration': 3.12}, {'text': 'The marble keeps moving along its circular\\npath.', 'start': 235.86, 'duration': 2.4}, {'text': 'But to you, it looks like it\u2019s just moving\\nback and forth along a straight line.', 'start': 238.26, 'duration': 3.739}, {'text': 'Not only that, but it looks like this marble\\nis stopping momentarily as it changes direction,', 'start': 241.999, 'duration': 4.58}, {'text': 'and moving faster as it gets closer to the\\nmiddle.', 'start': 246.579, 'duration': 2.59}, {'text': 'Which is exactly the same way the ball was\\nmoving on the spring.', 'start': 249.169, 'duration': 2.63}, {'text': 'Now, let\u2019s take this comparison a step further.', 'start': 251.799, 'duration': 2.601}, {'text': 'Let\u2019s assume that the radius of the ring is the same as the amplitude of the ball\u2019s motion on the spring.', 'start': 254.4, 'duration': 4.839}, {'text': 'And the marble\u2019s constant speed along the ring is equal to the maximum speed of the ball on the spring.', 'start': 259.24, 'duration': 4.22}, {'text': 'In that case, if you did the math, you\u2019d find that the equation for the marble\u2019s velocity', 'start': 263.46, 'duration': 3.76}, {'text': '-- when you look at it edge-on -- is exactly the same as the equation that described', 'start': 267.22, 'duration': 3.58}, {'text': 'the velocity of the ball on the spring.', 'start': 270.81, 'duration': 1.65}, {'text': 'So, let\u2019s recall what we know about uniform circular motion, to see what it can tell us about simple harmonic motion.', 'start': 272.46, 'duration': 5.54}, {'text': 'We know that the time it takes for the marble\\nto move around the ring once is called the period.', 'start': 278.0, 'duration': 4.54}, {'text': 'We also know that the period will be equal to the circumference of the ring, divided by the marble\u2019s speed.', 'start': 282.54, 'duration': 4.7}, {'text': 'And! The radius of the circle is the same\\nas the ball\u2019s amplitude on the spring.', 'start': 287.24, 'duration': 4.18}, {'text': 'So its circumference will be equal to two times pi times the amplitude.', 'start': 291.42, 'duration': 4.12}, {'text': 'This means that the period will be equal to\\n2 times pi times the amplitude,', 'start': 295.54, 'duration': 3.98}, {'text': 'divided by the marble\u2019s speed -- which, again, is the same as the ball\u2019s maximum speed as it moves on the spring.', 'start': 299.52, 'duration': 5.42}, {'text': 'And we can simplify that equation, since we\\nknow that the maximum speed of the ball is', 'start': 304.949, 'duration': 4.36}, {'text': 'equal to the (amplitude) times (the square\\nroot of the spring constant) divided by the (mass).', 'start': 309.309, 'duration': 4.691}, {'text': 'So: the period of the marble\u2019s motion around\\nthe ring is equal to (two pi) times (the root of m) over (k).', 'start': 314.009, 'duration': 5.842}, {'text': 'Now, we\u2019ve also talked about the frequency\\nof uniform circular motion:', 'start': 319.86, 'duration': 3.62}, {'text': 'It\u2019s the number of revolutions the marble makes around the ring every second, and it\u2019s equal to 1, divided by the period.', 'start': 323.48, 'duration': 6.72}, {'text': 'In this case, the frequency will also be equal\\nto 1 over (2 pi) times (the square root of k) over (m).', 'start': 330.2, 'duration': 6.64}, {'text': 'And that\u2019ll apply to the ball on the spring,\\ntoo.', 'start': 336.84, 'duration': 2.04}, {'text': 'Because the rules are the same!', 'start': 338.88, 'duration': 1.42}, {'text': 'Finally, there\u2019s angular velocity to consider.', 'start': 340.3, 'duration': 2.46}, {'text': 'In uniform circular motion, we\u2019ve described\\nit as the number of radians per second that', 'start': 342.77, 'duration': 3.639}, {'text': 'the marble covers as it moves around the ring.', 'start': 346.409, 'duration': 2.56}, {'text': 'And angular velocity is just equal to the\\nfrequency times 2 pi.', 'start': 348.969, 'duration': 3.56}, {'text': 'Which means that in the case of the ball on the spring, it\u2019s equal to the square root of k over m.', 'start': 352.529, 'duration': 4.551}, {'text': 'So now, with the help of our knowledge about\\ncircular motion, we can understand the period,', 'start': 357.09, 'duration': 4.359}, {'text': 'frequency, and angular velocity of the ball\u2019s simple harmonic motion as it oscillates on the spring.', 'start': 361.449, 'duration': 5.322}, {'text': 'But there\u2019s one more question: How does\\nthe ball\u2019s position change over time?', 'start': 366.78, 'duration': 4.56}, {'text': 'To find out, we\u2019ll have to analyze the\\nmarble\u2019s motion along the ring again.', 'start': 371.34, 'duration': 3.26}, {'text': 'And the answer will involve some trigonometry.', 'start': 374.6, 'duration': 2.46}, {'text': \"But it\u2019s not particularly complicated trig so, it'll be fine.\", 'start': 377.06, 'duration': 3.16}, {'text': 'At any given point along the marble\u2019s path, it\u2019ll be at a certain angle to the right-hand side of the ring.', 'start': 380.22, 'duration': 4.9}, {'text': 'And the cosine of that angle will be equal to its horizontal distance from the center of the ring, divided by the ring\u2019s radius.', 'start': 385.12, 'duration': 5.84}, {'text': 'We already know that the radius of the ring is the same as the amplitude of the ball\u2019s motion along the spring.', 'start': 390.96, 'duration': 4.84}, {'text': 'And if you turn the ring so that it looks\\nlike a line again, you can see that the marble\u2019s', 'start': 395.81, 'duration': 4.1}, {'text': 'horizontal distance from the center of the ring is the same as the ball\u2019s distance from the equilibrium point.', 'start': 399.91, 'duration': 4.749}, {'text': 'So, the cosine of theta is equal to the (ball\u2019s\\nposition) divided by its (amplitude).', 'start': 404.659, 'duration': 4.331}, {'text': 'In other words, the ball\u2019s position is equal\\nto (the amplitude), times (the cosine of the angle).', 'start': 408.99, 'duration': 4.06}, {'text': 'And we can simplify this equation, too.', 'start': 413.05, 'duration': 1.869}, {'text': 'In the same way that distance is equal to\\nvelocity multiplied by time,', 'start': 414.92, 'duration': 3.88}, {'text': 'the angle is equal to the angular velocity multiplied by time.', 'start': 418.8, 'duration': 3.82}, {'text': 'So, we can write the equation for the position\\nof the ball as x = A cos w t.', 'start': 422.62, 'duration': 4.359}, {'text': 'And when you graph this equation, something interesting happens: It looks like a wave!', 'start': 426.98, 'duration': 4.519}, {'text': 'We\u2019ll be talking a lot more about waves\\nin our next three episodes.', 'start': 431.499, 'duration': 2.84}, {'text': 'But for now, it\u2019s helpful just to see the\\nconnection here:', 'start': 434.34, 'duration': 3.54}, {'text': 'For an object in simple harmonic motion, the graph of its position versus time is a wave.', 'start': 437.88, 'duration': 5.26}, {'text': 'Which is why the swaying of the Millennium\\nBridge looked like a wave.', 'start': 443.14, 'duration': 3.34}, {'text': 'Speaking of the bridge: now we can better\\nunderstand what happened to it.', 'start': 446.49, 'duration': 2.81}, {'text': 'The bridge\u2019s shimmy was the result of oscillation, but it was made worse by another culprit: resonance.', 'start': 449.3, 'duration': 5.44}, {'text': 'Resonance can increase the amplitude of an oscillation by applying force at just the right frequency --', 'start': 454.74, 'duration': 5.24}, {'text': 'kind of like how you can get a kid to swing higher by pushing at just the right moment.', 'start': 459.98, 'duration': 5.2}, {'text': 'The engineers of the Millennium Bridge were\\nreminded of that, the hard way.', 'start': 465.18, 'duration': 3.41}, {'text': 'When pedestrians on the bridge started to\\nlean into its swaying, they created resonance.', 'start': 468.59, 'duration': 4.58}, {'text': 'They amplified the amplitude of the oscillation.', 'start': 473.17, 'duration': 2.74}, {'text': 'And the engineers of the bridge did account for oscillations caused by resonance when they designed it.', 'start': 475.91, 'duration': 4.43}, {'text': 'But they only considered vertical oscillations -- the kind that would have made the bridge bounce up and down.', 'start': 480.34, 'duration': 5.159}, {'text': 'They didn\u2019t realize that they\u2019d also have to factor in the horizontal swaying caused by people walking.', 'start': 485.5, 'duration': 4.68}, {'text': 'So, it was only a tiny bit of swaying at first, but it got a lot worse because people were leaning into their steps, causing resonance.', 'start': 490.18, 'duration': 5.799}, {'text': 'In the end, engineers had to apply a series of changes to the bridge that applied force to counteract its oscillations.', 'start': 495.98, 'duration': 5.24}, {'text': 'Because if there\u2019s one thing you don\u2019t\\nwant your bridge to be doing, it\u2019s The Wave.', 'start': 501.22, 'duration': 3.58}, {'text': 'Today, you learned about simple harmonic motion -- the energy of that motion, and how we can use math', 'start': 504.8, 'duration': 4.36}, {'text': 'of uniform circular motion to find the period, frequency, and angular velocity of a mass on a spring.', 'start': 509.16, 'duration': 5.42}, {'text': 'We also described how the position of an object in simple harmonic motion changes over time.', 'start': 514.58, 'duration': 5.34}, {'text': 'Crash Course Physics is produced in association\\nwith PBS Digital Studios. You can head over', 'start': 519.92, 'duration': 4.64}, {'text': 'to their channel to check out amazing a playlist of the latest episodes from shows like First Person, PBS Game Show, and The Good Stuff.', 'start': 524.57, 'duration': 6.84}, {'text': 'This episode of Crash Course was filmed in\\nthe Doctor Cheryl C. Kinney Crash Course Studio', 'start': 531.41, 'duration': 4.35}, {'text': 'with the help of these amazing people and\\nour equally amazing graphics team, is Thought Cafe.', 'start': 535.76, 'duration': 4.7}]",
    "concept": [
      {
        "start": 64.5,
        "end": 67.62,
        "concept description": "Simple harmonic motion: Oscillations follow a particular, consistent pattern."
      },
      {
        "start": 104.52,
        "end": 109.86,
        "concept description": "Energy in simple harmonic motion: Kinetic energy and potential energy interplay as the ball compresses and stretches the spring."
      },
      {
        "start": 272.46,
        "end": 282.54,
        "concept description": "Period of simple harmonic motion: Time it takes for one complete oscillation, derived from uniform circular motion."
      }
    ]
  },
  {
    "title": "Simple Harmonic Motion: Hooke's Law",
    "description": "Springs are neat! From slinkies to pinball, they bring us much joy, and now they will bring you even more joy, as they help you ...",
    "thumbnail": "https://i.ytimg.com/vi/gZ_KnZHCn4M/default.jpg",
    "videoId": "gZ_KnZHCn4M",
    "transcript": "[{'text': \"Professor Dave here, let's discuss simple\", 'start': 0.0, 'duration': 2.7}, {'text': 'harmonic motion.', 'start': 2.7, 'duration': 1.3}, {'text': 'Sometimes when we examine the motion of', 'start': 10.68, 'duration': 1.98}, {'text': 'an object, it will involve a', 'start': 12.66, 'duration': 1.47}, {'text': 'single action, like a rock falling from a', 'start': 14.13, 'duration': 2.37}, {'text': 'cliff down to the ground.', 'start': 16.5, 'duration': 1.65}, {'text': 'This will probably just happen one time', 'start': 18.15, 'duration': 2.1}, {'text': 'after which the rock will remain at rest.', 'start': 20.25, 'duration': 2.699}, {'text': 'But some motion is periodic, meaning', 'start': 22.949, 'duration': 3.451}, {'text': 'repeated, like the motion of the pendulum', 'start': 26.4, 'duration': 2.129}, {'text': 'on a grandfather clock, or the vibration', 'start': 28.529, 'duration': 2.82}, {'text': 'of a spring. We will refer to this kind', 'start': 31.349, 'duration': 2.521}, {'text': 'of motion as simple harmonic motion. Say', 'start': 33.87, 'duration': 3.779}, {'text': 'we have a spring that is attached to', 'start': 37.649, 'duration': 1.621}, {'text': 'some stationary surface, and on the other', 'start': 39.27, 'duration': 2.4}, {'text': 'end of the spring there is a block of a', 'start': 41.67, 'duration': 1.95}, {'text': 'particular mass. If we pull this block so', 'start': 43.62, 'duration': 2.88}, {'text': 'as to expand the spring and then we', 'start': 46.5, 'duration': 2.16}, {'text': 'release the block, it will vibrate back', 'start': 48.66, 'duration': 2.309}, {'text': 'and forth between more compressed and', 'start': 50.969, 'duration': 2.34}, {'text': 'less compressed states. If we assume that', 'start': 53.309, 'duration': 3.511}, {'text': 'the surface of motion is completely', 'start': 56.82, 'duration': 2.129}, {'text': 'frictionless, then the elastic potential', 'start': 58.949, 'duration': 2.13}, {'text': 'energy reaches a maximum when the spring', 'start': 61.079, 'duration': 2.611}, {'text': 'is most or least compressed and the', 'start': 63.69, 'duration': 2.67}, {'text': 'block is changing direction, while', 'start': 66.36, 'duration': 2.009}, {'text': 'kinetic energy is at a maximum when the', 'start': 68.369, 'duration': 2.311}, {'text': 'block is right in the middle and moving', 'start': 70.68, 'duration': 2.31}, {'text': 'the fastest. If we were to graph the', 'start': 72.99, 'duration': 2.489}, {'text': 'position of the block against time it', 'start': 75.479, 'duration': 2.401}, {'text': 'would display sinusoidal behavior, just', 'start': 77.88, 'duration': 3.12}, {'text': 'like a trigonometric sine function, where', 'start': 81.0, 'duration': 2.43}, {'text': 'the block continues to occupy the same', 'start': 83.43, 'duration': 2.52}, {'text': 'positions over a particular period of', 'start': 85.95, 'duration': 2.61}, {'text': 'time, which is why we call this periodic', 'start': 88.56, 'duration': 3.15}, {'text': 'motion. x equals 0 at the equilibrium', 'start': 91.71, 'duration': 3.33}, {'text': 'position of the block, where it was at', 'start': 95.04, 'duration': 2.369}, {'text': 'before we pulled it, and assuming zero', 'start': 97.409, 'duration': 2.161}, {'text': 'friction the block will oscillate', 'start': 99.57, 'duration': 2.1}, {'text': 'between positive x and negative x', 'start': 101.67, 'duration': 2.909}, {'text': 'indefinitely. In reality, frictional', 'start': 104.579, 'duration': 2.671}, {'text': \"forces will dampen the spring's activity\", 'start': 107.25, 'duration': 2.07}, {'text': 'and it will eventually come to a stop,', 'start': 109.32, 'duration': 1.74}, {'text': 'but for many systems an ideal', 'start': 111.06, 'duration': 2.46}, {'text': 'mass-spring system will be a decent', 'start': 113.52, 'duration': 2.82}, {'text': 'approximation for a real one. Of course', 'start': 116.34, 'duration': 3.12}, {'text': 'every spring is different, some are loose', 'start': 119.46, 'duration': 2.31}, {'text': 'like a slinky and some are stiff like', 'start': 121.77, 'duration': 1.949}, {'text': 'the spring that launches a pinball into', 'start': 123.719, 'duration': 1.711}, {'text': 'play. This factor is represented by the', 'start': 125.43, 'duration': 2.52}, {'text': 'spring constant k, which will be unique', 'start': 127.95, 'duration': 2.399}, {'text': 'to a particular spring.', 'start': 130.349, 'duration': 2.041}, {'text': 'The force that a spring can exert is equal', 'start': 132.39, 'duration': 1.95}, {'text': 'to negative k times the displacement of', 'start': 134.34, 'duration': 2.16}, {'text': 'the object it acts upon, and this', 'start': 136.5, 'duration': 1.89}, {'text': \"relationship is called Hooke's law.\", 'start': 138.39, 'duration': 2.89}, {'text': 'The negative sign indicates that the force', 'start': 141.28, 'duration': 2.02}, {'text': 'of the spring is always opposite the', 'start': 143.31, 'duration': 2.19}, {'text': 'direction of the movement of the object.', 'start': 145.5, 'duration': 1.68}, {'text': 'When the object compresses the spring it', 'start': 147.18, 'duration': 2.76}, {'text': 'will push out, and when the object', 'start': 149.94, 'duration': 1.83}, {'text': 'stretches the spring it will pull in.', 'start': 151.77, 'duration': 2.85}, {'text': 'In both cases, the spring is attempting', 'start': 154.62, 'duration': 2.49}, {'text': 'to move the object back to its', 'start': 157.11, 'duration': 1.98}, {'text': 'equilibrium position, which is why the', 'start': 159.09, 'duration': 2.31}, {'text': 'force applied by the spring can be', 'start': 161.4, 'duration': 2.1}, {'text': 'called a restoring force. The units on a', 'start': 163.5, 'duration': 3.93}, {'text': 'spring constant will be Newtons per', 'start': 167.43, 'duration': 2.04}, {'text': 'meter, so that when you multiply by some', 'start': 169.47, 'duration': 2.46}, {'text': 'distance x, you get the force that must', 'start': 171.93, 'duration': 2.55}, {'text': 'be applied to compress that spring that far.', 'start': 174.48, 'duration': 2.98}, {'text': \"Let's also note that the elastic\", 'start': 178.68, 'duration': 1.5}, {'text': 'potential energy of a spring will be', 'start': 180.18, 'duration': 1.77}, {'text': 'equal to one-half kx squared, where k is', 'start': 181.95, 'duration': 3.21}, {'text': 'the spring constant and x is the', 'start': 185.16, 'duration': 2.07}, {'text': 'distance it is stretched or compressed.', 'start': 187.23, 'duration': 2.27}, {'text': 'If at equilibrium the distance is zero, so it', 'start': 189.54, 'duration': 3.02}, {'text': 'has zero elastic potential energy, and', 'start': 192.57, 'duration': 2.73}, {'text': 'the maximum elastic potential energy', 'start': 195.3, 'duration': 1.74}, {'text': 'will occur at the maximum distance from', 'start': 197.04, 'duration': 2.61}, {'text': 'this point on either side of the', 'start': 199.65, 'duration': 1.89}, {'text': 'oscillation. This expression looks', 'start': 201.54, 'duration': 2.759}, {'text': 'similar to the expression for kinetic', 'start': 204.299, 'duration': 1.681}, {'text': 'energy, which is convenient since the two', 'start': 205.98, 'duration': 2.52}, {'text': 'will interchange as the mass oscillates.', 'start': 208.5, 'duration': 2.74}, {'text': 'A pendulum also displays periodic motion', 'start': 212.72, 'duration': 2.58}, {'text': 'since it swings back and forth between', 'start': 215.31, 'duration': 1.89}, {'text': 'the same two positions,', 'start': 217.2, 'duration': 1.65}, {'text': 'although this involves gravitational', 'start': 218.85, 'duration': 2.25}, {'text': 'potential energy rather than elastic', 'start': 221.1, 'duration': 2.34}, {'text': 'potential energy, and we will look at', 'start': 223.44, 'duration': 1.74}, {'text': \"this behavior next. Let's check comprehension.\", 'start': 225.18, 'duration': 2.92}, {'text': 'Thanks for watching, guys. Subscribe to my', 'start': 256.88, 'duration': 3.48}, {'text': 'channel for more tutorials, support me on', 'start': 260.37, 'duration': 1.889}, {'text': 'patreon so I can keep making content, and', 'start': 262.259, 'duration': 2.31}, {'text': 'as always feel free to email me:', 'start': 264.569, 'duration': 1.56}]",
    "concept": [
      {
        "start": 33.87,
        "end": 50.969,
        "concept description": "Explanation of simple harmonic motion using a mass-spring system, including the behavior of the block and the spring's compression and expansion."
      },
      {
        "start": 132.39,
        "end": 138.39,
        "concept description": "Introduction to Hooke's Law, which states that the force exerted by a spring is equal to negative k times the displacement of the object."
      },
      {
        "start": 178.68,
        "end": 208.5,
        "concept description": "Elastic potential energy of a spring, given by the formula 1/2 kx^2, and its relationship with kinetic energy during oscillation."
      }
    ]
  },
  {
    "title": "Simple Harmonic Motion",
    "description": "Follow us: https://www.instagram.com/7activestudio/ For more information: www.7activestudio.com 7activestudio@gmail.com ...",
    "thumbnail": "https://i.ytimg.com/vi/uM2HpLBVAkA/default.jpg",
    "videoId": "uM2HpLBVAkA",
    "transcript": "[{'text': 'simple harmonic motion let us discuss', 'start': 6.64, 'duration': 9.69}, {'text': 'about s hm observe this simple pendulum', 'start': 11.54, 'duration': 8.46}, {'text': 'the resting position of the bob is known', 'start': 16.33, 'duration': 8.349}, {'text': 'as mean position one complete to and fro', 'start': 20.0, 'duration': 7.23}, {'text': 'movement of pendulum about its mean', 'start': 24.679, 'duration': 6.201}, {'text': 'position is known as an oscillation or', 'start': 27.23, 'duration': 8.7}, {'text': 'vibration observe these points in simple', 'start': 30.88, 'duration': 7.54}, {'text': 'pendulum simple pendulum oscillates', 'start': 35.93, 'duration': 6.92}, {'text': 'about its mean position acceleration and', 'start': 38.42, 'duration': 8.75}, {'text': 'displacements are in opposite directions', 'start': 42.85, 'duration': 7.24}, {'text': 'acceleration should always be directed', 'start': 47.17, 'duration': 7.36}, {'text': 'towards its midpoint in other words the', 'start': 50.09, 'duration': 7.35}, {'text': 'above are the conditions for a body to', 'start': 54.53, 'duration': 10.919}, {'text': 'be in SH M definition of SH M a body is', 'start': 57.44, 'duration': 10.89}, {'text': 'said to be in simple harmonic motion if', 'start': 65.449, 'duration': 6.211}, {'text': 'it moves to and fro about its mean', 'start': 68.33, 'duration': 6.89}, {'text': 'position such that at any point its', 'start': 71.66, 'duration': 6.6}, {'text': 'acceleration is directly proportional to', 'start': 75.22, 'duration': 6.72}, {'text': 'its displacement in magnitude but', 'start': 78.26, 'duration': 7.08}, {'text': 'opposite in direction and is directed', 'start': 81.94, 'duration': 7.35}, {'text': 'always towards the mean position', 'start': 85.34, 'duration': 3.95}, {'text': 'mechanical wave Soundwave in this', 'start': 90.659, 'duration': 8.861}, {'text': 'example a mechanical wave like sound', 'start': 95.619, 'duration': 7.32}, {'text': 'wave propagates as a result of simple', 'start': 99.52, 'duration': 6.599}, {'text': 'harmonic oscillations of the particles', 'start': 102.939, 'duration': 7.41}, {'text': 'of the medium projection of a particle', 'start': 106.119, 'duration': 7.53}, {'text': 'performing uniform circular motion on a', 'start': 110.349, 'duration': 6.87}, {'text': 'circumference of the circle make same', 'start': 113.649, 'duration': 6.93}, {'text': 'displacement in same intervals of time', 'start': 117.219, 'duration': 5.841}, {'text': 'T', 'start': 120.579, 'duration': 2.481}, {'text': 'you', 'start': 128.289, 'duration': 2.06}, {'text': 'vibrations of a tuning fork in this', 'start': 138.51, 'duration': 8.35}, {'text': 'example the vibrations of a tuning fork', 'start': 143.2, 'duration': 7.26}, {'text': 'oscillates about its mean position that', 'start': 146.86, 'duration': 6.87}, {'text': 'is by the definition its vibrations are', 'start': 150.46, 'duration': 9.24}, {'text': 'in SH M oscillations of a liquid column', 'start': 153.73, 'duration': 11.81}, {'text': 'in a u-tube in this example in u-tube', 'start': 159.7, 'duration': 9.18}, {'text': 'liquid oscillates about it mean position', 'start': 165.54, 'duration': 9.97}, {'text': 'that is its oscillation is in SH M these', 'start': 168.88, 'duration': 10.44}, {'text': 'are different examples of SH M the', 'start': 175.51, 'duration': 6.48}, {'text': 'following are the conditions for a body', 'start': 179.32, 'duration': 7.53}, {'text': 'to be in SH M 1 the motion should be', 'start': 181.99, 'duration': 8.75}, {'text': 'periodic about a fixed point to', 'start': 186.85, 'duration': 6.99}, {'text': 'acceleration and displacements should', 'start': 190.74, 'duration': 7.9}, {'text': 'always be in opposite directions 3 the', 'start': 193.84, 'duration': 7.47}, {'text': 'acceleration should always be directed', 'start': 198.64, 'duration': 7.04}, {'text': 'towards the fixed mean position', 'start': 201.31, 'duration': 4.37}]",
    "concept": [
      {
        "start": 57.44,
        "end": 85.34,
        "concept description": "Definition of Simple Harmonic Motion (SHM): A body is in SHM if it moves to and fro about its mean position such that its acceleration is directly proportional to its displacement in magnitude but opposite in direction and is always directed towards the mean position."
      },
      {
        "start": 90.659,
        "end": 102.939,
        "concept description": "Mechanical Wave Example: A mechanical wave like a sound wave propagates as a result of simple harmonic oscillations of the particles of the medium."
      },
      {
        "start": 138.51,
        "end": 165.54,
        "concept description": "Examples of SHM: Vibrations of a tuning fork and oscillations of a liquid column in a U-tube, both oscillate about their mean positions and are examples of SHM."
      }
    ]
  }
]