Question

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion ?
(a) a = 0.7 x
(b) a = -200x${}^2$
(c) a = - 10x
(d) a = 100x${}^3$

Answer 1

The correct option is (c) $a=-10x$

$F=-kx$

$ma=-kx$

$a=\frac{-kx}{m}$

For SHM, acceleration should be directly proportional to displacement and sign should be negative. Hence, (c) represents SHM.