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

Which one of the following equations of motion represents simple harmonic motion?
  1. Acceleration $=-\mathrm{k}_0 \mathrm{x}+\mathrm{k}_1 \mathrm{x}^2$
  2. Acceleration $=-\mathrm{k}(\mathrm{x}+\mathrm{a})$
  3. Acceleration $=\mathrm{k}(\mathrm{x}+\mathrm{a})$
  4. Acceleration $=\mathrm{kx}$ where $\mathrm{k}_1 \mathrm{k}_0, \mathrm{k}_1$ and are all positive.

Solution

Key Idea Acceleration $\propto$ - (displacement). $\begin{aligned} & A \propto-y \\ & A=-\omega^2 y \\ & A=-\frac{k}{m} y \\ & A=-k y \end{aligned}$ Here, $y=x+a$ $\therefore \text { acceleration }=-\mathrm{k}(\mathrm{x}+\mathrm{a})$ *

Asked in: NEET 2009 (Screening)

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