Question

ow long must a simple pendulum be if it is to make exactly ten swings per second? (That is, one complete vibration takes exactly 0.200 s.)

Answer 1

The period T of a pendulum is given by:

`T=2 \pi \sqrt{ (L)/(g) }`
where L is the length of the pendulum while
`g=9.81 m/s^2` is the gravitational acceleration.

In the pendulum of the problem, one complete vibration takes exactly 0.200 s, this means its period is
`T=0.200 s`. Using this data, we can solve the previous formula to find L:

`L=g ( (T)/(2\pi) )^2=(9.81 m/s^2)( (0.2 s)/(2 \pi) )^2=1 \cdot 10^(-3) m=1 mm`