The displacement time graph of an oscillating particle. Find the maximum velocity  of the particle.

For simple harmonic motion, the velocity of a particle is given by  $v=Aw\cos \left(wt\right)$ .  Hence the maximum velocity of the particle is $v_{\max }=A\omega$ . From the graph, time  period of oscillation is 0.2 s. Using the relation  $\omega =\frac{2\pi }{T}$ 
Hence,  $v_{\max }=A\omega =0.2\left(\frac{2\pi }{0.2}\right)=2\pi m{s}^{-1}$