It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.

The following are the two cases when body is executing S.H.M. The first case represents when body is moving in left direction and second represents when body is moving in right direction.

The graph shown below is plotted between the displacement and the force. The first and second quadrant represent the case (A). The third and fourth quadrant represents the case (B).