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$\bullet$ $\bullet$ In the laboratory, a student studies a pendulum by graphing the angle $\theta$ that the string makes with the vertical as a function of time $t,$ obtaining the graph shown in Figure 11.39 . (a) What are the period, frequency, angular frequency, and amplitude of the pendulum's motion? (b) How long is the pendulum? (c) Is it possible to determine the mass of the bob?

a) $1.6 \mathrm{s}, 0.625 \mathrm{Hz}, 3.93 \mathrm{rad} / \mathrm{s}$ and 6b) 0.635 $\mathrm{m}$c) can't be determine.

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

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in this problem, we have a graph that looks something like this. The first step is to read off attributes of the periodic motion based on the graph. And so the quickest and easiest one to read off is the amplitude we can see based on this value here that the attitudes about six degrees and we can also read off the period quite easily. The period is the amount of time for to do one cycle, which is that right there and so we can see that the period is 1.6 seconds. Now, from these two things, we can ascertain some other things. For instance, we confined at the frequency is equal to the one over a period playing in 1.60 point 1.60 6 to 5 and then the units on this or it hurts. If the units on the period arm seconds as they are now, annual frequency is equal to two pi times f. So now we can use this what? White by two pi. And when you do that, we get 3.93 ratings for second. These air, the four pieces of information we need to complete party for part B. We want to figure out what the length of the pendulum must be. To do that, we can use this equation. The period is equal to two pi tests for of the length or Grammy. And now we can solve this for the length to get gravity times t over to pie squared. We just found what t wasn't party, so we can plug that in. And when we do that, we get 0.635 meters for Percy. It is asking if we can determine the mass of the blob of the Bob from the graph, and we cannot because Period here is independent of the mass so we can read off the period from the graph. But that doesn't tell us anything about the mass because the mass is involved in this relationship. So the answer is no.

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