The mechanical energy of a SHM oscilator:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{{\mathbf{v}}}_{{\mathbf{x}}}}^{{\mathbf{2}}}}$ where (1/2)kA^{2} is the total energy E, (1/2)kx^{2} is the potential energy U, and (1/2)mv_{x}^{2} is the kinetic energy K.

A harmonic oscillator has angular frequency ω and amplitude *A*.

At an instant when the displacement is equal to *A*/2, what fraction of the total energy of the system, *E*, is kinetic, and what fraction is potential?

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