spring is stretched by a distance $\frac{\mathrm{L}}{2} \theta .$ Therefore

restoring force is spring $=\mathrm{K}\left(\frac{\mathrm{L}}{2} \theta\right) .$ Each spring

causes a torque $\tau(=\mathrm{Fd})=\left(\frac{\mathrm{KL} \theta}{2}\right) \frac{\mathrm{L}}{2}$ in the

same direction.

Therefore equation of ratational motion is $\tau=I \alpha$

$-2\left(\frac{\mathrm{KL} \theta}{2}\right) \frac{\mathrm{L}}{2}=\mathrm{I} \alpha$ with $\mathrm{I}=\frac{\mathrm{ML}^{2}}{12}$

$\alpha=-\left(\frac{6 K}{M}\right) \theta$

Standard equation of angular $S.H.M.$ is

$\alpha=-\omega^{2} \theta$

$\omega^{2}=\frac{6 \mathrm{K}}{\mathrm{M}}$

frequency $\quad \mathrm{f}=\frac{\omega}{2 \pi}=\frac{1}{2 \pi} \sqrt{\frac{6 \mathrm{K}}{\mathrm{M}}}$