The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (c) the period? (d) the angular frequency of this motion?

Question

Graph depicting the displacement of an oscillating object as a function of time in simple harmonic motion.

Accepted Answer

Hey everyone in this problem. The variation of the displacement with time for vibrating mass is shown in the graph below and were asked to determine the frequency and angular frequency for the vibration. Alright. So we're given the graph we have X and centimeters on the Y axis time T. In seconds on the X axis. Okay, now we're asked to determine the frequency and angular frequency. Were given a position time graph or displacement time graph like this. The easiest value to pick out is the period T. Okay. Now let's recall that we can relate the frequency F to the period through the inverse. So the frequency is going to be one over the period. T. Okay, so let's go ahead and find that period T. That's going to allow us to find our frequency F. All right, so when we're looking for the period we wanna look for two consecutive points where the graph is in the same position. What do I mean by that? So let's choose this point where we're at zero. Mhm. Let me draw this in red. Maybe we're at zero and we want to do one full cycle. Okay, so we go up to the maximum, back to zero. This is not going to be one full period. Okay, When we chose our first point we were at zero and our position was increasing. Okay, at this position, our position is decreasing. Okay, so this is not the next value we're looking for. Okay, we're gonna go down to our minimum and now we're at zero and increasing again. And so this is going to be our full period from red dot to red dot. Okay. We go up to our maximum down to our minimum and then we're back to our starting position. Alright So the period T. It's gonna be the time between these two. Okay so it's gonna be that final time minus the initial time In this case the final time is 13.8 seconds. The initial time is 1.8 seconds which gives us a period t. of 12 seconds. Alright so we found the period T. Which is gonna allow us to find the frequency and again the frequency is gonna be one over the period T. Which is going to be 1/12 seconds which gives us a frequency of 0.833 hertz. Alright so we found the frequency and now we're asked to find the angular frequency as well. Now let's recall that the angular frequency omega is going to be equal to two pi F. Or equivalently to two pi over the period T. You can use either value whether you want to use the period T. The frequency f. Either one will work fine. Let's just use the period T. And we have two pi over 12 seconds which gives us an omega value of approximately 0.5-4 in the unit radiance per second. Alright so our frequency 0.833 hurts our angular frequency 0.5 to four radiance per second. And if we look at our answer choices, we see that we have answer choice C. Okay, F. Is equal to 0.833 hertz, and omega is equal to 0.5 to four radiance per second. Thanks everyone for watching. I hope this video helped see you in the next one.

The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (c) the period? (d) the angular frequency of this motion?

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Key Concepts

Period

Angular Frequency

Simple Harmonic Motion (SHM)