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?

gaby131o
2022-09-22
Answered

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

Answered 2022-09-23
Author has **12** answers

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

$T=2\times 3.14\times \sqrt{\frac{0.2m}{9.8m{s}^{-2}}}=0.9s$

The object will reach its highest speed at the lowest point of its trajectory - and this will be at a time given by $\frac{T}{4}\approx 0.22s$

$2\pi \sqrt{\frac{l}{g}}$

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

$T=2\times 3.14\times \sqrt{\frac{0.2m}{9.8m{s}^{-2}}}=0.9s$

The object will reach its highest speed at the lowest point of its trajectory - and this will be at a time given by $\frac{T}{4}\approx 0.22s$

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