Question

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

Answer 1

Correct Answer - 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)`