The x-t graph of a particle undergoing simple harmonic motion is shown below.  The acceleration of the particle at t =$\frac{4}{3}\sec$ is

From the graph, time period, T = 8 sec.
Equation of motion is
$\begin{array}{l}\mathrm{x}\left(\mathrm{cm}\right)=\left(1\mathrm{cm}\right)\sin \left(\frac{2\pi }{8}\mathrm{t}\right)\\ \mathrm{v}=\frac{\pi }{4}\cos \left(\frac{\pi }{4}\mathrm{t}\right)\\ \mathrm{a}=-{\left(\frac{\pi }{4}\right)}^2\sin \left(\frac{\pi }{4}\mathrm{t}\right)\\ \text{ At }\mathrm{t}=\frac{4}{3}\sec ,\mathrm{a}=-\left(\frac{{\pi }^2}{16}\right)\sin \left(\frac{\pi }{4}\frac{4}{3}\right)=-\frac{\sqrt{3}}{32}{\pi }^2\mathrm{cm}/{\mathrm{s}}^2.\end{array}$