question_answer

What fraction of the total energy is kinetic when the displacement of a simple harmonic oscillator is half of its amplitude?

Answer:

                \[\frac{\text{Kinetic energy}}{\text{Total energy}}=\frac{\frac{1}{2}m{{\omega }^{2}}\left( {{A}^{2}}-\frac{{{A}^{2}}}{4} \right)}{\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}}=\frac{\mathbf{3}}{\mathbf{4}}\]