Question

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

Answer 1

pi/3 ?

Answer 2

let me double check tho

Answer 3

it won't let me answer in that form

Answer 4

well period is how often it repeats

Answer 5

never mind it was 6

Answer 6

are you sure it is 6?

Answer 7

yeah it is 6

Answer 8

\[d=2\sin\left(\frac{\pi t}{3}\right)\]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 \(2\pi\).\[\frac{\pi T}{3}=2\pi \Rightarrow \boxed{T=6}\]

Answer 9

just take whataver t is multiplied by and and divide 2pi by it

2pi/(pi/3)=6