Oscillations - Result Question 11

14. Which one of the following equations of motion represents simple harmonic motion?

[2009]

(a) Acceleration $=-k(x+a)$

(b) Acceleration $=k(x+a)$

(c) Acceleration $=kx$

(d) Acceleration $=-k_0 x+k_1 x^{2}$ where $k, k_0, k_1$ and a are all postive.

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Answer:

Correct Answer: 14. (a)

Solution:

  1. (a) acceleration, $a=-kX$, where, $X=x+a$.

In simple harmonic motion acceleration is directly proportional to the displacement from the mean position. Also the acceleration is in the opposite direction of displacement.