The total mechanicla energy of a spring mass sytem in simple harmonic motion is `E=1/2momega^2 A^2`. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude `A` remains the same. The new mechanical energy will

Options

A. becomes `2E`
B. become `E//2`
C. become `sqrt2E`
D. remain `E`

Answer

B

Explanation

`omega=sqrt(k/m)`, `omega^'=sqrt((k)/(2m))=(omega)/(sqrt2)`
`E^'=1/2*2momega^('^2)A^2=m(omega/sqrt2)^2A^2=1/2momega^2A^2=E/2`