Energy in Simple Harmonic Motion Video Lessons

Concept

# Problem: A harmonic oscillator has angular frequency ω and amplitude A.What are the magnitudes of the displacement and velocity when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) (Use any variable or symbol stated above as necessary.)x =v =

###### FREE Expert Solution

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.

Angular frequency:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\sqrt{\frac{\mathbf{k}}{\mathbf{m}}}}$

(a)

U = K = (1/2)E

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###### Problem Details

A harmonic oscillator has angular frequency ω and amplitude A.

What are the magnitudes of the displacement and velocity when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) (Use any variable or symbol stated above as necessary.)
x =
v =