Question

A 45 lb. child enjoys swinging very high. If the length of the chain that holds the swing is 2.5 M, approximately how often should the child be pushed to get a good, high swing? Hint: determine the natural frequency for the child.

Answer 1

A child's playgroung swing is an example of a simple pendulum.

We treat the child as the bob.

Let us look at the picture which shows the child on swing

Since we need the child to have a good swing,that is to have a large amplitude,the child has to be pushed at his natural frequency. (When this happens,that is when the system is being driven at a natural frequency of oscillation the result is oscillations of larger amplitude.This phenomenon is called resonance (for this reason natural frequencies are sometimes called resonant frequencies))

So now let's find out the natural frequency of the child

  

where L is the length of the chain=2.5m(given)

g is 9.8m/s

Now,

= 0.30272 Hz

We know that,time period,

= 3.3033 seconds

Therefore, the has to be pushed once in every 3 seconds.