A body is executing a simple harmonic motion such that its potential energy is U1 at x and U2 at y. When the displacement is x+y , the potential energy will be

At displacement x, U1 = 12mω2x2⇒ x= 2U1mω2Similarly, y = 2U2mω2When displacement is (x+y), potential energy isU = 12mω2(x+y)2 = 12mω2(x2+y2+2xy)     = 12mω2x2+12mω2y2+mω2xy      = U1+U2+mω22U1mω2.2U2mω2     = U1+U2+U1U22