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{ (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 (T^2)/((2 \pi)^2)=(9.81 m/s^2) ((0.333 s)^2)/((2 \pi)^2)=0.028 m`