Which of the following relationship between the acceleration, a and the displacement x of a particle involve simple harmonic motion.
(a) `a=7.0x` (b) `a=-200x^(2)` (c) `a=-10x` (d) `a=100x^(3)`

Explanation

To determine which of the given relationships between acceleration \( a \) and displacement \( x \) involves simple harmonic motion (SHM), we need to analyze each option based on the fundamental condition for SHM.

In SHM, the acceleration \( a \) is directly proportional to the displacement \( x \) and is always directed towards the equilibrium position. This can be mathematically expressed as:

\[ a = -k x \]

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