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

For simple harmonic motion, the acceleration of a particle is given by   $a=-A{w}^2\sin \left(wt\right)$ .

 Hence the maximum acceleration of the particle is  $a_{\max }=A{\omega }^2$. 

 From the graph, time period of oscillation is 5 s. Using the relation $\omega =\frac{2\pi }{T}$  
 $$\begin{gathered} maximumu acceleration=a_{\max }=A{\omega }^2 \\ \Rightarrow a_{\max }=5{\left(\frac{2\pi }{5}\right)}^2 \\ \Rightarrow a_{\max }=\frac{4{\pi }^2}{5}m{s}^{-2} \end{gathered}$$