Question

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

Answer 1

`~~0.22\ "s"`

Explanation:

The time period of a pendulum of length `l` is given by

`2pi sqrt(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((0.2\ "m")/(9.8\ "m"\ "s"^-2)) = 0.9\ "s"`

The object will reach its highest speed at the lowest point of its trajectory - and this will be at a time given by `T/4 ~~ 0.22\ "s"`