When you graph simple harmonic motion in an acceleration versus displacement graph, the graph at any point would be linear. The graph would also pass through the origin giving proportionality of acceleration to negative displacement. Definition of proportionality neglects the negative value of the displacement so therefore acceleration is proportional to displacement. The acceleration of the motion is always directed towards equilibrium and so at maximum displacement, there would be greatest negative acceleration and vise versa.At the origin, the displacement would be zero and acceleration would also be zero
