Maximum kinetic energy of a particle of mass 1 kg in SHM is 8 J. Time period of SHM is 4 s. Maximum potential energy during the motion is 10 J. Then,

Maximum kinetic energy = energy of oscillation in SHM

$\therefore 8=\frac{1}{2}k{A}^2$

$\therefore k{A}^2=16$ …… (i) 

Further,$2\pi \sqrt{\frac{m}{k}}=4$

$\therefore \frac{1}{k}=\frac{4}{{\pi }^2} or k=\frac{{\pi }^2}{4}$ … (ii)

From Eq. (i) and (ii), we get

k=24 N/m

And A=2.53 m

Maximum acceleration of the particle will be

$$\begin{gathered} a_{\max }={\omega }^{2}A=\frac{k}{m}A=\left(\frac{25}{1}\right)(2.53) \\ =6.3 \mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$