A body is executing S.H.M. At a displacement x its potential energy is 9 J and at a displacement y its potential energy is 16 J . The potential energy at displacement x + y is

Step-by-step solution

Consider an oscillating spring-mass system. Potential energy at displacement x will be written as, 1 2 k x 2 . Now, 1 2 k x 2 = 9       . . . E q 1 and 1 2 k y 2 = 16       . . . E q 2 Then, potential energy at the displacement is given by, = 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 2 1 2 k y 2 = 9 + 16 + 2 × 3 × 4 = 49   J