An object in simple harmonic motion has position function s(t)...

Question

An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.

𝒮(t) = 5 cos 2t

What is the frequency?

Accepted Answer

Hey, everyone in this problem, a student is performing a simple harmonic motion experiment using the equation SFT is equal to eight cosine of three T where SFT is the position in feet and T is the time in seconds. We're asked to find the frequency of the motion. We're given four answer choices. Option A two pi divided by three cycles per second. Option B three divided by two pi cycles per second. Option C pi divided by four cycles per second and option D four divided by pi cycles per second. So let's start by rewriting our equation. SFT is equal to eight cosine of three T. And what we wanna find is the frequency. Now, the frequency we can't get directly from our equation but recall that the frequency is related to the period and the period is something we can find from our equation. So the frequency is going to be one divided by the period. OK. It's the reciprocal of the period. Now cosine the function cosine has a period of two pi. So the period of our function SFT is going to be that original period of just cosine of T on its own divided by the B value in our function. Now the B value recall is the coefficient attached to the T inside of the brackets here inside of the, attached to the variable inside of the brackets. OK. It's that number being multiplied out in front of the variable inside of our brackets. So in this case, we have that B is equal to three. OK? Because inside the brackets, we have three T and so the period for our function is going to be equal to two pi divided by three. Now, we have to be careful. Remember the question is asking for the frequency, not the period. So two pi divided by three is not our answer. And the answer is going to be the reciprocal of that. OK. The frequency is going to be equal to one divided by two pi divided by three. And so this gives us a frequency of three divided by two pi cycles per second. OK? Because our time was in seconds. And so this is the final frequency that we were looking for in this problem. If we go up to our answer choices and compare what we found, we can see that option B is the correct answer. That's it for this one. Thanks everyone for watching. See you in the next video.

An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the frequency?

Key Concepts

Simple Harmonic Motion (SHM)

Frequency

Angular Frequency

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