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=Awcoswt .  Hence the maximum velocity of the particle is vmax=Aω . From the graph, time  period of oscillation is 0.2 s. Using the relation  ω=2πT Hence,  vmax=Aω=0.22π0.2=2π  ms−1