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) + 2 sqrt(U_(1)U_(2))`

Answer

D

Explanation

`U_(1) = (1)/(2) m omega^(2) y_(1)^(2)`
`U_(2) = (1)/(2) m omega^(2) y_(2)^(2)`
`U = (1)/(2) m omega^(2) (y_(1) + y_(2))^(2) = (sqrt(U_(1)) + sqrt(U_(2)))^(2)`