Question
A simple pendulum performs S.H.M. about x = 0 with an amplitude a and time period T. What is the speed of the pendulum at $\text{x}=\frac{\text{A}}{2}?$
✓
Answer
Velocity of oscillating body $=\text{v}=\omega\sqrt{\text{A}^2-\text{x}^2}$$\text{x}=\frac{\text{A}}{2}$
$\text{v}=\omega\sqrt{\text{A}^2-\Big(\frac{\text{A}^2}{4}\Big)}$
$=\frac{\sqrt{3}\text{A}\omega}{2}=\frac{\sqrt{3}\text{A}\pi}{\text{T}}$
$\text{v}=\omega\sqrt{\text{A}^2-\Big(\frac{\text{A}^2}{4}\Big)}$
$=\frac{\sqrt{3}\text{A}\omega}{2}=\frac{\sqrt{3}\text{A}\pi}{\text{T}}$
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