A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7

shows a graph of the ball's position x as a function of time t. What are the oscillation's (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?

Video transcript

Everyone in this problem. We have a 1.6 kg block fixed to one end of a spring. The motion of the block is monitored and the position as a function of time is graphed below. Were asked to determine the period and frequency of the oscillation. All right now, the graph we're given, we see that the position X. Is given in centimeters on the Y axis and the time t in seconds on the X axis. Alright, so we're thinking about the period. Okay, we want to look at the amount of time it takes to go from one spot on this curve, all the way back and around to the exact same spot. Okay. So if we consider starting at the why access here. Okay, you can see that our graph goes down all the way back up and we reach the same point. Okay, a full period right here at this max height. And if we look on our graph, okay, we have 12 and each of these markings is .2. So this is going to be at 1.2 seconds. Alright, so to go from this point all the way down and back to the exact same point. That's going to be one period. Okay. And so are period T is going to be equal to 1.2 seconds. Okay, because we start at zero seconds and we go to 1.2 seconds. It's a total of 1.2 seconds. Alright, so we found our period T. Now we need to find the frequency. Well let's recall that the frequency is related to the period through inverse. So the frequency is going to be one over the period T. It's gonna be 1/1.2 seconds. She's gonna give us a frequency of 0.833 repeated. Um In our unit here is hurts. Alright? So if you look at our answer traces, okay? We found a period of 1.2 seconds and the frequency of 0.3 sorry 0.83 hertz. We have answer E. That's it for this one. Thanks everyone for watching. See you in the next video.