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. become 2 E
B. become 4E
C. become `sqrt(2)E`
D. remain same

Answer

D

Explanation

`T=2pisqrt((m)/(k))`
`implies omega=sqrt((k)/(m)) implies k=momega^(2)`
as spring constant k remain same
`therefore`total energy `E=(1)/(2)kA^(2)` remain same.