# Problem: 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?

###### FREE Expert Solution

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)kA2 is the total energy E, (1/2)kx2 is the potential energy U, and (1/2)mvx2 is the kinetic energy K.

97% (225 ratings) ###### Problem Details

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?