The potential energy of a particle of mass 4 kg in motion along the x -axis is given by U =4(1- cos 4 x) J. The time period of the particle for small…

The potential energy of a particle of mass $\displaystyle 4$ kg in motion along the $\displaystyle x$-axis is given by $\displaystyle \mathrm{U}=4(1-\cos 4 x) \mathrm{J}$. The time period of the particle for small oscillation $\displaystyle (\sin \theta \simeq \theta)$ is $\displaystyle \left(\frac{\pi}{\mathrm{K}}\right) s$. The value of K is \_\_\_\_.