Rankers Physics
Topic: Oscillation

Which one of the following equations of motion represents simple harmonic motion? (2009)nwhere $k$, $k_0$, $k_1$ and $a$ are all positive.
Acceleration $= -k(x)$
Acceleration $= k(x + a)$
Acceleration $= kx$
Acceleration $= -k_0x + k_1x^2$

Solution:

For simple harmonic motion, the acceleration must be directly proportional and opposite in direction to the displacement. Thus, $a \propto -x$, which matches the equation $\text{Acceleration} = -k(x)$.

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