13. oscillations — Physics STD 11 Science — Question

Velocity is maximum at mean position i.e. $x=0$

$\Rightarrow \sin \left(2 \pi t+\frac{\pi}{3}\right)=0$

$\Rightarrow\left(2 \pi t+\frac{\pi}{3}\right)=0, \pi, 2 \pi, 3 \pi \dots$

if we take $\left(2 \pi t+\frac{\pi}{3}\right)=0,$ time will come negative which is not possible. So we take $\left(2 \pi t+\frac{\pi}{3}\right)=\pi$

$\Rightarrow t=\frac{1}{3} s=0.33 s$

for other solutions, we will get higher values of time. but since it is asking for the first time after $t=0,$ the required solution will be $t=0.33 s$