Question

A spring-mass oscillator has a total energy $E_0$ and an amplitude $x_0$. How large will $K$ and $U$ be for it when $x=\frac{1}{2}{x}_0$?

Answer 1

Total energy, $E_0=\frac{1}{2}k{x}_0^2$

Now, potential energy, $U=\frac{1}{2}k{x}^2=\frac{1}{4}k{x}_0^2=\frac{E_0}{2}$

And since $E_0=K+U$

Kinetic energy, $K=E_0-U=\frac{E_0}{2}$