Question

Find the length of a pendulum that oscillates with a frequency of 0.16 hz. the acceleration due to gravity is 9.81 m/s 2 . answer in units of m.

Answer 1

The period of the pendulum is the reciprocal of the frequency:
$T= \frac{1}{f}= \frac{1}{0.16 Hz}=6.25 s$

The period of the pendulum is given by
$T=2 \pi \frac{L}{g}$
where L is the length of the pendulum, and g the acceleration of gravity. By re-arranging the formula and using the value of T we found before, we can  calculate the length of the pendulum L:
$L=g \frac{T^2}{(2 \pi)^2}=(9.81 m/s^2) \frac{(6.25 s)^2}{(2 \pi)^2}=9.71 m$