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Mathematics
OpenStudy (anonymous):

For the simple harmonic motion equation d=2sin(pi/3t) , what is the period?

OpenStudy (anonymous):

pi/3 ?

OpenStudy (anonymous):

let me double check tho

OpenStudy (anonymous):

it won't let me answer in that form

OpenStudy (anonymous):

well period is how often it repeats

OpenStudy (anonymous):

never mind it was 6

OpenStudy (anonymous):

are you sure it is 6?

OpenStudy (anonymous):

yeah it is 6

OpenStudy (anonymous):

\[d=2\sin\left(\frac{\pi t}{3}\right)\]The period \(T\) is defined as the time it takes for the function to repeat itself, thus, if we substitute \(t \mapsto t+T\), we should have the same function.\[d=2\sin\left(\frac{\pi (t+T)}{3}\right)\equiv2\sin\left(\frac{\pi t}{3} + \frac{\pi T}{3}\right)\]Now, since the sine function repeats every \(2\pi\), we can thus reason that the extra term here is equal to \(2\pi\).\[\frac{\pi T}{3}=2\pi \Rightarrow \boxed{T=6}\]

OpenStudy (anonymous):

just take whataver t is multiplied by and and divide 2pi by it 2pi/(pi/3)=6

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