Question

A particle performs linear SHM of amplitude 5 cm at what displacement from its mean position will the potential energy of the particle be 20% of the total energy

Answer 1

The total energy is

$$T=\frac12kA^2.$$

The potential energy corresponding to a position that results in being 20% of the total energy is

$$P=\frac12kd^2=0.2T.\\\space\\ \frac12kd^2=0.2\cdot\frac12kA^2,\\\space\\ d^2=0.2A^2,\\ d=A\sqrt{0.2}=5\sqrt{0.2}=2.24\text{ cm}.$$