Energy in Simple Harmonic Motion Video Lessons

Concept

# Problem: An object of mass m is attached to a spring having force constant k. The object oscillates with simple harmonic motion. Its maximum displacement from equilibrium is A. What is the total mechanical energy of the spring/mass system when the object is located at x = +A

###### FREE Expert Solution

The mechanical energy of a spring system undergoing simple harmonic motion:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{K}}{\mathbf{+}}{\mathbf{U}}}$

Potential energy:

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{{\mathbf{v}}}_{{\mathbf{x}}}}^{{\mathbf{2}}}}$

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###### Problem Details

An object of mass m is attached to a spring having force constant k. The object oscillates with simple harmonic motion. Its maximum displacement from equilibrium is A. What is the total mechanical energy of the spring/mass system when the object is located at x = +A