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

Answer

A

Explanation

P.E. at a displacement x is `E_(1)=(1)/(2)Kx^(2)`
`therefore x=sqrt((2E_(1))/(K))`
and `E_(2)=(1)/(2)Ky^(2) therefore y=sqrt((2E_(2))/(K))`
and `E=(1)/(2)K(x+y)^(2) therefore x+y=sqrt((2E)/(K))`
`because sqrt((2E_(1))/(K)) +sqrt((2E_(2))/(K))=sqrt((2E)/(K))`
`therefore sqrt(E_(1))+sqrt(E_(2))=sqrt(E )`