shm definition

Question

In simple harmonic motion, acceleration is proportional to?

RankGuru · Accepted Answer

1. **Definition of SHM**: Simple Harmonic Motion is a special type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
2. **Mathematical Form**: $F = -k x$.
3. **Acceleration ($a$)**: From Newton's Second Law, $a = \frac{F}{m} = -\frac{k}{m} x$.
4. **Equation**: $a = -\omega^2 x$, where $\omega = \sqrt{k/m}$ is the angular frequency.
5. **Analysis**: The equation shows $a \propto x$ (magnitude) and the negative sign indicates it is directed toward the mean position, hence **opposite to displacement**.

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shm definition

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