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 amplitude 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 find the amplitude of the motion for our answer choices. A says it's 8 ft. B says 3 ft, C says 4 ft and D says 11 ft. Now we're trying to find the amplitude of our motion. And if we look at the function that represents the simple harmonic motion experiment, we notice that it's a cosine function. So what do we know about the cosine and amplitude? Well, recall that every cosine function is written in the general form a multiplied by the cosine of B multiplied by X minus C by that expression plus D OK. Where A is the amplitude off? That phone B helps us to find the period of that function. Because the period of the cosine function equals two pi divided by B or the magnitude of B C tells us the phase shift of that function. That is how much it moves horizontally to the left or right and D tells us the vertical shift of that function that is how much it moves up and down. So if we can compare our function that represents the harmonic motion experiment to the general form of a cosine function, then we will be able to find the amplitude. Because notice here, the amplitude is really just the coefficient of the cosine term. So let's go ahead and do that. So given our function we are here, our, our, our function is SF T equals it multiplied by the cosine of three T. Right then notice that from our expression, our amplitude, that is the coefficient of the cosine term is eight. So right away here, we can tell that our amplitude A equals it. Therefore, the amplitude of the motion is 8 ft. When we look back on our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helps.

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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 amplitude of this motion?