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Uniform and Non-Uniform Motion

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Question

Starting from the extreme position, the time taken by an ideal simple pendulum to travel a distance of half the amplitude is

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Solution

The quantity $\phi = wt+\delta$ is called the phase . It determines the status of the particle in simple harmonic motion
$x= A\sin \left ( wt +\delta \right )\rightarrow$ phase
$x=\cos \omega t = \frac{A}{2}=A\cos \omega t$
$\frac{1}{2} = \cos \omega t = \omega t = \frac{\pi }{3}$
$\frac{2\pi }{T} t = \frac{\pi }{3} = t = T/6$

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