For a body performing simple harmonic motion, its potential energy is E_x at displacement x and E _ y at displacement y from mean position. The potential energy E ₀ at displacement ( x + y ) is

Step-by-step solution

Potential energy at x = E _ x = 1 2 kx ^2 x = 2 E _ x k Similarly, Potential energy at y = E _ y = 1 2 ky ^2 y= 2 E_y k P.E. at displacement ( x + y )= E = 1 2 k ( x + y )^2 array ll & E= 1 2 k (x^2+y^2+2 x y ) & E= k 2 [ 2 E₁ k + 2 E₂ k + 2 2 E₁ E₂ k ] & E=E_x+E_y+2 E_x E_y array