Question

When you push a child on a swing, your action is most effective when your pushes are time to concide with the natural frequency of the motion. You are swinging a 30 kg child on a swing suspended from 5 meter cables. Estimate the optimum time interval between your pushes.
Would your answer be different if the child had a different mass?

Answer 1

Answer:

4.4857 seconds

No

Explanation:

L = Length of the pendulum = 5 m

g = Acceleration due to gravity = 9.81 m/s²

Time period is given by

$T=2\pi\sqrt{\dfrac{L}{g}}\\\Rightarrow T=2\pi\sqrt{\dfrac{5}{9.81}}\\\Rightarrow T=4.4857\ s$

The optimum time interval in between the pushes is 4.4857 seconds

It can be seen that the mass of the child is not used in the formula and hence changing the mass would not result in a different time period.

The length of the pendulum and the acceleration of gravity of the planet determines the time period.