In this problem, we are required to carry out analysis on the energy transformation in a simple harmonic oscillator.

The mechanical energy of an SHM oscillator:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{{\mathbf{v}}}_{{\mathbf{x}}}}^{{\mathbf{2}}}}$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.

Part A. When the displacement of a mass on a spring is 1/2A the half of the amplitude, what fraction of the energy is kinetic energy?

Part B. At what displacement, as a fraction of A, is the energy half kinetic and half potential?

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Our tutors have indicated that to solve this problem you will need to apply the Energy in Simple Harmonic Motion concept. You can view video lessons to learn Energy in Simple Harmonic Motion. Or if you need more Energy in Simple Harmonic Motion practice, you can also practice Energy in Simple Harmonic Motion practice problems.