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?

1 Answer
May 14, 2018

#~~0.22\ "s"#


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"#