Two simple harmonic motions `y_1=Asinomegat` and `y_2=Acosomegat` are supre imposed on a particle of mass m.

Options

A. `(1)/(2)momega^2A^2`
B. `momega^2A^2`
C. `(1)/(4)momega^2A^2`
D. zero

Answer

B

Explanation

`y_1=Asinomegat`
`y_2=Asihn(omegat+(pi)/(2))`
`A_X=A`
`a^y=A`
`a=`resultant amplitude`=sqrt(a_x^2+a_y^2)`
`=sqrt(A^2+A^2)=sqrt2A`
`E=(1)/(2)ma^2omega^2`
`=(1)/(2)m2a^2omega^2` or `E=mA^2omega^2`