A body is executing simple harmonic motion. At a displacement `x` its potential energy is `E_(1)` and at a displacement `y` its potential energy is `E_(2)` The potential energy `E` at displacement `(x+y)` is

Options

A. `sqrt(E)=sqrt(E_(1))-sqrt(E_(2))`
B. `sqrt(E)=sqrt(E_(1))+sqrt(E_(2))`
C. `E=E_(1)+E_(2)`
D. `E=E_(1)-E_(2)`

Answer

B

Explanation

`E_(1)=(1)/(2)kx^(2)impliesx=sqrt((2E_(1))/(k)),E_(2)=(1)/(2)ky^(2)impliesy=sqrt((2E_(2))/(k))`
and `E=(1)/(2)k(x+y)^(2)impliesx+y=sqrt((2E)/(k))`
`impliessqrt((2E_(1))/(k))+sqrt((2E_(2))/(k))=sqrt((2E)/(k))impliessqrt(E_(1))+sqrt(E_(2))=sqrt(E)`