The mass is shown in figure is resting on a frictionless horizontal table. Each of two

identical springs has force constant k and unstretched length lo . At equilibrium the mass rests at the

origin and the distances a are not necessarily equal to lo . Show that when the mass moves to a

position(x,y) with x and y small the potential energy has the form U=1/2[kxx2

+kyy2

], for an

anisotropic oscilator. Show that if a< lo the equilibrium at the origin is unstable and explain why.