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Vilka [71]
3 years ago
15

What is the magnitude of the velocity when the elastic potential energy is equal to the kinetic energy? (Assume that U=0 at equi

librium.)
Physics
1 answer:
zhannawk [14.2K]3 years ago
6 0

Answer:

Explanation:

General Equation of SHM is given by

x=A\cos \omega t

v=-A\omega \sin \omega t

where x=position of particle

A=maximum Amplitude

\omega =angular frequency

t=time

At any time Total Energy is the sum of kinetic Energy and Elastic potential Energy i.e. \frac{1}{2}kA^2

where k=spring constant

Potential Energy is given by U=\frac{1}{2}kx^2

also it is given that Potential Energy(U) is equal to Kinetic Energy(K)

Total Energy=K+U

Total=2U=2\times \frac{1}{2}kx^2

\frac{1}{2}kA^2=2\times \frac{1}{2}kx^2

x=\pm \frac{A}{\sqrt{2}}

at x=\frac{A}{\sqrt{2}}

velocity is v=\frac{A\omega}{\sqrt{2}}

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