The potential energy of a particle of mass 0.1text{ kg} executing simple harmonic motion is given by U = 5x^2text{ J}, where x is displacement in met…

Potential energy in SHM is $U = \frac{1}{2}kx^2$. Comparing with $U = 5x^2$, we get $\frac{1}{2}k = 5 \implies k = 10\text{ N/m}$. Angular frequency $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{10}{0.1}} = \sqrt{100} = 10\text{ rad/s}$. Frequency $f = \frac{\omega}{2\pi} = \frac{10}{2\pi} = \frac{5}{\pi}\text{ Hz}$.