Question

A particle performs S.H.M. Its potential energies are 'U₁' and 'U₂' at displacements 'x₁' and 'x₂' respectively. At displacement (x₁ + x₂), its potential energy 'U' is ______.

Options

• `sqrtU=(sqrtU_1+sqrtU_2)^2`

• `sqrtU=(sqrtU_1-sqrtU_2)^2`

• `sqrtU=sqrtU_1+sqrtU_2`

• `sqrtU=sqrtU_1-sqrtU_2`

Answer 1

A particle performs S.H.M. Its potential energies are 'U₁' and 'U₂' at displacements 'x₁' and 'x₂' respectively. At displacement (x₁ + x₂), its potential energy 'U' is `underline(sqrtU=sqrtU_1+sqrtU_2)`.

Explanation:

`U_1=1/2kx_1^2`     `thereforex_1=sqrt((2U_1)/"k")`

`U_2=1/2kx_2^2`     `thereforex_2=sqrt((2U_2)/"k")`

`therefore U=1/2k(x_1+x_2)^2`

`thereforex_1+x_2=sqrt((2U)/"k")`

`sqrt((2U_1)/"k")+sqrt((2U_2)/"k")=sqrt((2U)/"k")`

`thereforesqrtU=sqrtU_1+sqrtU_2`