Answer
$T = \frac{1}{\omega}$
Work Step by Step
$V = a~sin~(2\pi~\omega~t)$
We can find the period $T$:
$2\pi~\omega~T = 2\pi$
$T = \frac{2\pi}{2\pi~\omega}$
$T = \frac{1}{\omega}$
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