The displacement of an oscillating object as a function of time is shown in Fig. E14.4

. What is (a) the frequency? (b) the amplitude? (c) the period? (d) the angular frequency of this motion?

Video transcript

Everyone in this problem, we have a graph that shows displacement as a function of time for a vibrating mass and were asked to determine the period and amplitude of the vibration. Okay, Alright, so we're given the displacement in centimeters and the time in seconds. Alright. The first thing we want to find is the period T. And when we're looking for the period T from a graph, what we want to do is we want to pick out two points where the graph is in the same position. Okay, And look at the time between them. Alright, so we want to pick out two points. So let's choose here. Okay, well we are at a displacement of zero at four seconds and we want to go through one full cycle for our period. So we want to go up to our maximum down to our minimum and then back to the same position we were in before. Okay, and that just that time between those two red dots is going to represent one period. Now a common mistake to make is when you go up to this maximum. Okay, and you get back down to zero and when you consider that to be one period, that is not one full period. Because we're not back to the same place. We were what do I mean? Well we're at four seconds. Okay, our displacement is zero but the displacement is increasing. Okay, When we're at this 8.4 ish seconds. Okay, the displacement is also zero but it's decreasing. Okay, so that's not actually the same point. Okay, so we have to get all the way back through a maximum through a minimum and back to where our displacement is zero and we're increasing again. Okay. Alright so now we've picked two points that represent one full period in the period. T just going to be equal to the difference in those times. Okay, so it's gonna be the final time minus the initial time of those points we chose this is going to be 13 seconds -4 seconds. So we get a period of nine seconds. Alright so we found our period. Now we need to find the amplitude and the amplitude A is going to be the max displacement from X equals zero. Okay max displacement from X equals zero. Alright so if we look at this graph we have X equals zero. This line here, the X axis And we see that we get up to a maximum x value of 13cm. Okay and a minimum x value of negative 13cm. Okay so the maximum displacement from this axis. Okay, it's gonna be this distance here or this distance here. Okay. Either way it is 13 centimeters it is equal to 13 centimeters and it's important to remember that it's the displacement maximum displacement from X equals zero. Okay we're not taking that full distance from the maximum to the minimum. We're taking the displacement from zero. Okay so it's gonna be 13 centimeters. Alright so if we look at our answer choices, we see that we have answer choice E. Okay. We found a period of nine seconds in an amplitude of 13 cm. Thanks everyone for watching. I hope this video helped see you in the next one.