The equation of motion of a particle is given by \(x=a\sin (50t+\pi /3)cm\). The particle will come to rest at time \({t…

At rest (v = 0):

\(\cos (50t+\pi /3)=0\Rightarrow 50t+\pi /3=\frac{\pi }{2}\)\({t}_{1}=\frac{\pi /2-\pi /3}{50}=\frac{\pi }{300}\)

Acceleration \(\left(a=-{\omega }^{2}x\right)\) :

\(a=-2500a\sin (50t+\pi /3)\)

For zero acceleration:

\(\sin (50t+\pi /3)=0\Rightarrow 50t+\pi /3=\pi\)

\({t}_{2}=\frac{\pi -\pi /3}{50}=\frac{\pi }{75}\)