Question

Xa linear harmonic oscillator of force constant 2 x10 6 n/m and amplitude 0.01 m has a total mechanical energy of 100 j. its maximum potential energy

Answer 1

Must be 100 joules.

As the total mechanical energy is always conserved that means sum of Kinetic energy and Potential energy is always constant.
Potential energy is maximum iff Kinetic energy is minimum i.e. 0 .
mech. energy = pot.energy + Kinetic energy

100 = pot.energy + 0
hence
maximum potential energy is 100 J.