A particle is executing SHM. At a displacement `y_(1)` its potential energy is `U_(1)` and at a displacement `y_(2)` its potential energy is `U_(2)`. The potential energy of the particle at displacement `(y_(1)+y_(2))` is

Options

A. `U_(1)+U_(2)`
B. `sqrt(U_(1)^(2)+U_(2)^(2))`
C. `U_(1)-U_(2)`
D. `U_(1)+U_(2)+2sqrt(U_(1)U_(2))`

Answer

D

Explanation

Potential energy,
`U=(1)/(2)momega^(2)y^(2)`
`Upropy^(2)`
`U=K(y_(1)+y_(2))^(2)`
`=K(Y_(1)^(2)+Y_(2)^(2)+2y_(1)y_(2))`
`U=U_(1)+U_(2)+2sqrt(U_(1)U_(2))`