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.


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