Question

A mass is oscillating with amplitude A at the end of the spring. How far is this mass from the equilibrium if the elastic potential energy equals γ times the kinetic energy?

Answer 1

Mechanical energy is conserved

K+U=E

$E=\frac{1}{2}kA^2$ and $U=\frac{1}{2}kx^2$

E=U

$\frac{1}{2}kA^2=\frac{1}{2}kA^2 \implies x=\frac{x}{\sqrt{2}}$