Energy in Simple Harmonic Motion Video Lessons

Concept

# 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.

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###### 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?

What scientific concept do you need to know in order to solve this problem?

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.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Li's class at UH.