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  4. A particle performs simple harmonic motion about X=0 with an amplitude A and time period T. The speed of the particle at X=(A/2) will be

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Q. A particle performs simple harmonic motion about $X=0$ with an amplitude $A$ and time period $T$. The speed of the particle at $X=\frac{A}{2}$ will be

Solution:

Velocity of a particle executing S.H.M. is given by
$v=\omega \sqrt{a^{2}-x^{2}}=\frac{2 \pi}{T} \sqrt{A^{2}-\frac{A^{2}}{4}}$
$=\frac{2 \pi}{T} \sqrt{\frac{3 A^{2}}{4}}=\frac{\pi A \sqrt{3}}{T}$