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

Step-by-step solution

For a body executing SHM, aligned & E₁= 1 2 k x^2, E₂= 1 2 k y^2 & E= 1 2 k(x+y)^2= 1 2 k (x^2+y^2+2 x y ) & = 1 2 k x^2+ 1 2 k y^2+2 [ 1 2 k( x y )^2 ] & =E₁+E₂+2 E₁ E₂ = ( E₁ + E₂ )^2 & E = E₁ + E₂ aligned