Describe simple harmonic motion (SHM). Sketch a displacement-time graph for a particle undergoing SHM and the corresponding velocity-time and acceleration-time graphs. Use these graphs to describe the relationship between accleration and displacment.

Simple harmonic motion is periodic motion in which a restoring force acts in the opposite direction to that of displacement and is directly proportional to the displacement.The displacement-time graph for SHM should be of sinusoidal form. As should the velocity-time and acceleration-time graphs but should be shifted by a half/full period in the x-direction respectively.Acceleration-time graph flipped in x-axis compared to displacement-time graph. Therefore, acceleration is in the opposite direction but equal in magnitude (hence directly proportional) to displacement. Student should recognise that restoring force = mass * acceleration hence, relate these statements to those in the definition of SHM above.