Question

How long must a simple pendulum be if it is to make exactly six swings per second? (that is, one complete vibration takes exactly 0.333 s.)?

Answer 1

The period of a simple pendulum is given by:
$T=2 \pi \sqrt{ \frac{L}{g} }$
where L is the length of the pendulum and g is the gravitational acceleration.

The pendulum in our problem makes one complete vibration in 0.333 s, so its period is T=0.333 s. Using this information, we can re-arrange the previous formula to find the length of the pendulum, L:
$L= g \frac{T^2}{(2 \pi)^2}=(9.81 m/s^2) \frac{(0.333 s)^2}{(2 \pi)^2}=0.028 m$