Physics - SHM Question with Solution | TestHub

$\mathrm{Using\; the\; general\; equation\; of\; SHM}$

$x=\mathrm{A}\sin \mathrm{\omega }\mathrm{t}$

as per graph A = 1 cm, T = 8 sec

$\begin{array}{l}\Rightarrow w=\frac{2\pi }{\mathrm{T}}=\frac{\pi }{4}\\ x=\sin \frac{\pi }{4}t\\ acceleratio\mathrm{n }a=\frac{d^{2}x}{d{t}^2}\\ \Rightarrow a=\frac{-{\pi }^2}{16}\sin \frac{\pi }{4}t\\ at\mathrm{ t}=\frac{2}{3},a=\frac{-{\pi }^2}{16}\sin \left(\frac{\pi }{4}.\frac{2}{3}\right)=\frac{-{\pi }^2}{16}.\sin \left(\frac{\pi }{6}\right)\\ \Rightarrow a=\frac{-{\pi }^2}{16}\times \frac{1}{2}=\frac{-{\pi }^2}{32}cm/s^2\end{array}$