# A simple pendulum has length 20cm.it was displaced at an angle 15^o and then released to execute simple harmonic motion. How much time is required for the pendulum to reach maximum speed?

A simple pendulum has length 20cm.it was displaced at an angle ${15}^{\circ }$ and then released to execute simple harmonic motion. How much time is required for the pendulum to reach maximum speed?
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Mario Dorsey
The time period of a pendulum of length l is given by
$2\pi \sqrt{\frac{l}{g}}$
While this formula is valid only for small angles of oscillation, this works pretty well for an amplitude of ${15}^{\circ }$ (in fact the error between the "exact" time period and this one becomes 1% only when the amplitude is ${23}^{\circ }$). For the present case, we have
$T=2×3.14×\sqrt{\frac{0.2m}{9.8m{s}^{-2}}}=0.9s$
The object will reach its highest speed at the lowest point of its trajectory - and this will be at a time given by $\frac{T}{4}\approx 0.22s$