The total mechanical energy of a spring mass system 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. become 2E
B. become `E//2`
C. become `sqrt(2)E`
D. remain E

Answer

D

Explanation

`E=(1)/(2)momega^(2)A^(2)=(1)/(2)m(sqrt((k)/(m)))^(2)A^(2)`
`E=(1)/(2)kA^(2)`
Total energy depends on k of spring and amplitude A. It is independent of mass.