Spring potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

The potential energy of the system is maximum when the displacement is maximum. Maximum displacement is equal to A.

Figure 1 shows a harmonic oscillator at four different moments, labeled A, B, C, and D.

Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. We will also assume that there are no resistive forces so the total energy of the oscillator remains constant.

What is the maximum potential energy of the system?