You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (a) How much time does it take the pendulum bob to reach its highest speed?

Video transcript

Everyone in this problem, we have a simple pendulum has a length of 1.35 m. The pendulum is displaced to one side by 5.6° and allowed to oscillate And were asked to determine the time taken from the time it is launched to the time its acceleration is equal to zero. Alright, so let's think about this. Okay, when this is launched, okay, when the pendulum is launched it is going to be at its amplitude, that maximum displacement. So when launched, pendulum is at the amplitude a amplitude. Okay, so we know that we're starting at the amplitude A Where are we? Kind of finishing this measure of time? We're gonna look when the acceleration is zero. Okay, what is the acceleration? 0? Okay well the acceleration is equal to zero At equilibrium. Okay recall that when we get to equilibrium, the acceleration is going to be zero and equilibrium is when we are at X equals zero. So we want to take the time. So we want the time from X equals the amplitude A two x equals equilibrium zero. Well know that this is going to be Equal to the period T divided by a four. If you think you can think about this as like a sine wave. So think of a sine wave to go from the amplitude which would be here, A 20 is a quarter of your period. Right? Because down here It's going to be negative a that's gonna be happier period and then all the way back up to positive a would be a full period. Okay, so to go from 8-0 is a quarter of your period. So it's 2/4. Okay, so we know that the time taken from launch to the acceleration of zero is gonna be T over four. Okay. So we just need to go ahead and find the period T. So that we can calculate to over four. Well we're given the length of the pendulum. Let's recall how we can relate the period T to the length of the pendulum. Two pi over. T. Is equal to the square root of G over L. Okay. And so are period T is going to be equal to two pi times the square root of L. Over G. Let's give ourselves a little bit more room to write. So we have two pi times the square root of the length L which is 1.35 m The length of the pendulum given in the problem divided by G. The gravitational acceleration in this case it's for Earth. So it's just 9.8 m per second squared. Ok. That regular G that we use and if you work this out on our calculator we get that the period T is equal to 2.332 seconds. Okay. Alright, so be careful here it can be enticing to go and answer the question 2.332 seconds. But remember this was our period T. That we found. What we're trying to find is the time taken to go from the amplitude to the equilibrium. Okay. From when we launched, when the acceleration is zero, which is T over four. Okay, so what we really want to calculate is T over four, Which is 2.332 seconds divided by four, Which gives us 0.583 seconds. Okay. Alright. So if we go back up to our answer choices, we see that the time taken from the time that the pendulum is launched to the time its acceleration of zero is going to be answered. D 0.583 seconds. Thanks everyone for watching. I hope this video helped see you in the next one.