Question

When you push a child on a swing, your action is most effective when your pushes are timed to coincide 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:

$T = 4.48 s$

we can see that this time period is independent of the mass of the child so answer would be same if the child mass is different

Explanation:

Natural frequency of a simple pendulum of L length is given as

$f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$

so the time period of the oscillation is given as

$T = 2\pi \sqrt{\frac{L}{g}}$

so we will have

$L = 5 m$

$T = 2\pi\sqrt{\frac{5}{9.81}}$

$T = 4.48 s$

also from above formula we can see that this time period is independent of the mass of the child so answer would be same if the child mass is different