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A simple harmonic oscillator has amplitu...

A simple harmonic oscillator has amplitude A, angular velocity `omega`, and mass m . Then, average energy in one time period will be

A

`(1)/(4)m omega^(2)A^(2)`

B

`(1)/(2)m omega^(2)A^(2)`

C

`m omega^(2)A^(2)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A
Average energy `=(int_(0)^(T)"u dt")/(int_(0)^(T)dt)=(1)/(T)int_(0)^(T)"u dt"`
`=(1)/(2T)int_(0)^(T)momega^(2)A^(2)cos^(2)(omegat+phi)dt=(1)/(4)momega^(2)A^(2)`
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