A body is executing simple harmonic motion. At a displacement x its potential energy is E₁ and at a displacement y it potential energy is E₂ . The potential energy (E) at displacement (x+y) is

Step-by-step solution

Potential energy of a body executing SHM. aligned & U= 1 2 m ^2 y^2 & U₁= 1 2 m ^2 x^2 x= 2 U₁ m ^2 & and U₂= 1 2 m ^2 y^2 & y= 2 U₂ m ^2 & aligned At displacement (x+y) aligned & U= 1 2 m ^2(x+y)^2 & (x+y)= 2 U m ^2 & 2 U₁ m ^2 + 2 U₂ m ^2 = 2 U m ^2 & U₁ + U₂ = U & i.e. E = E₁ + E₂ & aligned