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QUESTION

Determine whether the function $f(t)=\sin(3t)$ is periodic and, if
so, find the smallest period.

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ANSWER

$f(t+T)=\sin(3(t+T))=\sin(3t+3T), \, =\sin(3t)$ if $3T=2n\pi$

i.e. $\ds T=\frac{2\pi n}{3},\ (n=1,2,3,\ldots)$

Therefore the function is periodic with minimum period
$\ds\frac{2\pi}{3}$.





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