Energy in Simple Harmonic Motion Video Lessons

Concept

# Problem: At what displacement of a SHO is the energy half kinetic and half potential?Express your answer in terms of amplitude A.

###### FREE Expert Solution

Total mechanical energy:

$\overline{)\begin{array}{rcl}{\mathbf{E}}& {\mathbf{=}}& \mathbf{P}\mathbf{.}\mathbf{E}\mathbf{+}\mathbf{K}\mathbf{.}\mathbf{E}\\ {\mathbf{E}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}\mathbf{k}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{\mathbf{v}}^{\mathbf{2}}\end{array}}$

Displacement at extreme ends is the same as amplitude, A.

91% (254 ratings)
###### Problem Details

At what displacement of a SHO is the energy half kinetic and half potential?