Question

Average energy in one time period of a simple harmonic oscillator whose amplitude is A, angular velocity is $\omega$ and mass is m is

• A.
• B.
• C.
• D. zero

Answer 1

The correct option is A

Average energy,
$<u>=\frac{{\int }_0^{T}udt}{{\int }_0^{T}dt}=\frac{1}{T}{\int }_0^{T}udt=\frac{1}{2T}{\int }_0^{T}m{\omega }^2{A}^2{\cos }^2(\omega t-\varphi )dt$
$=\frac{1}{4}m{\omega }^2{A}^2$