Answer
$T = 2\pi\sqrt{\frac{m}{k}}$
Work Step by Step
We find:
$ \frac{dx}{dt} = A\omega cos \omega t$
Thus, it follows:
$ \frac{d^2x}{dt^2} = -A\omega^2 sin \omega t$
Using equation 13.3 and the fact that $ x=Asin\omega t $, we find:
$m(-A\omega^2 sin \omega t)=-k Asin\omega t $
Since $ T = \frac{2\pi}{\omega}$, we find:
$T = 2\pi\sqrt{\frac{m}{k}}$
