Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
(a) a = 0.7x
(b) a = –200x2
(c) a = –10x
(d) a = 100x3
The relation between displacement and acceleration involves S.H.M when acceleration is proportional to displacement and is directed in the opposite direction.
In (c) acceleration is proportional to displacement x and directed in the opposite direction. Hence, only (c) a = –10x involves Simple Harmonic motion.