Question

A particle of mass m free to move in the x-y plane is subjected to a force whose components are F_x = - kx and F_y = - ky, where k is a constant. The particle is released when t = 0 at the point (2, 3). Prove that the subsequent motion is simple harmonic along the straight line 2y -3x = 0.

Answer 1

When it is displaced to a point P whose position vector is 

Since, 

motion is simple harmonic. At t = 0 particle is at (2,  3)

i.e., the particle will oscillate simple harmonically along this line.