Q.Potential energy of a particle performing linear S.H.M is $0.1\pi^2x^2$ joule (x in metre). If mass of the particle is 20 g, find the frequency of S.H.M.

[!TLDR] Comparing $E_p=0.1\pi^2x^2$ with $E_p=\frac12m\omega^2x^2$: $\omega^2=\frac{0.2\pi^2}{m}$. With m = 0.02 kg, $\omega=\pi\sqrt{10}\approx9.935$ rad …

The potential energy of an S.H.M. particle is $E_p=\frac12kx^2=\frac12m\omega^2x^2$ (Eq. 5.23). Given $E_p=0.1\pi^2x^2$ (x in metre, energy in joule), comparing coefficients: $\frac12m\omega^2=0.1\pi^2$, so $\omega^2=\frac{0.2\pi^2}{m}$. With $m=20$ g $=0.02$ kg, $\omega^2=\frac{0.2\pi^2}{0.02}=10\pi^2$, so $\omega=\pi\sqrt{10}\approx9. …

Match the coefficient of $x^2$ in the given potential-energy expression to $\frac12m\omega^2$, s …

Forgetting to convert the mass from grams to kilograms before substituting, which changes the fin …