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Two simple harmonic motions y(1) = Asino...

Two simple harmonic motions `y_(1) = Asinomegat` and `y_(2)` = Acos`omega`t are superimposed on a particle of mass m. The total mechanical energy of the particle is

A

`(1)/(2)momega^2A^2`

B

`momega^2A^2`

C

`(1)/(4)momega^2A^2`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
B
`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`
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