The displacement of simple harmonic oscillator after 3 seconds...

Displacement equation is given by $x = Asin\omegat$

Now, when amplitude is halved, $\dfrac{A}{2} = Asin\omegat$

Or $\omegat = \dfrac{\pi}{6}$

At, $t = 3s$, $\omega\left(3\right) = \dfrac{\pi}{6}$$⇒ \omega = \dfrac{\pi}{18}$

Time period, $T = \dfrac{2\pi}{\omega} = \dfrac{2\pi}{\dfrac{\pi}{18}} = 36s$