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 period of this motion?

Accepted Answer

Welcome back. Everyone. In this problem. A student is performing a simple harmonic motion experiment using the equation SF T equals eight multiplied by the cosine of three T where SF T is the position in feet and T is the time in seconds. We want to find a period of the motion for our answer choices A is two pi seconds. B is 1/4 of pi seconds. C is two thirds of pi seconds and D is a third of pi seconds. Now, if we want to find a period of the motion, and we notice here that the equation that describes the simple harmonic motion experiment is a cosine function, then we have to ask ourselves, how is the cosine related to the period of, of, of, of the motion? What do we know? Well, recall that the general form of the cosine function says that the cosine function is always equal to a multiplied by the cosine of B multiplied by the expression X minus C plus D. OK. Where A is the amplitude of our function B helps us to find the period of our, of our cosine function because the period equals two pi divided by the magnitude of B OK. See helps us to find a fierce shift of our function. That is how much it moves to the left or right. And D helps us to find our vertical shift D is the vertical shift. That is how much it moves up or down. So if we can compare the equation that we have to the general form, then we should be able to find B and thus, we should be able to solve for the period. So let's do that. So for the function that we have, which is SF T equals eight multiplied by the cosine of three T here, if we look at both these functions, then B which would represent the coefficient of either the expression X minus C or if C equals zero, then just the expression X B would be equal to three. OK. So B equals three, since B equals three, then that tells us the period is going to be equal to two pi divided by the magnitude of B which would just be three that tells us then that the period is two thirds of pi seconds. If we look back on our answer choices, that would be answer choice. C thanks a lot for watching everyone. I hope this video helped.

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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 period of this motion?