A particle is said to be executing simple harmonic motion, if the acceleration ‘a’ produced in it satisfies the following two conditions : (i) ‘a’ is directly proportional to the displacement (say y) from the mean position. i.e. a ∝ y. (ii) ‘a’is directed towards mean position i.e. acts opposite to the direction in which y increases. i.e. Mathematically $a = -\omega^2 y$ ...(i) where $\omega =$ angular frequency. (a) $a = 0.7x$ does not satisfy eqn. (i), so it does not represent simple harmonic motion.(b) $a = -200x^2$ , does not satisfy equation (i) hence it does not represent simple harmonic motion. (c) a = –10x, here x = displacement. It satisfies equation (i), so it represents simple harmonic motion. (d) $a = 100x^3$ does not satisfy equation (i), hence it does not represent simple harmonic motion.