Velocity Vs Displacement Shm

Question

Maximum speed occurs at what displacement in SHM?

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1. **Velocity-Displacement Equation**: $v(x) = \omega \sqrt{A^2 - x^2}$.
2. **Extreme Position ($x=A$)**: $v = \omega \sqrt{A^2 - A^2} = 0$. The particle stops and reverses.
3. **Mean Position ($x=0$)**: $v = \omega \sqrt{A^2 - 0} = \omega A$. 
4. **Conclusion**: The maximum speed occurs exactly at the **mean position (zero displacement)**.
5. **Analogy**: Like a pendulum swing, the bob is fastest as it passes through the bottom (center) and slowest at the highest points of its arc.

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Velocity Vs Displacement Shm

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