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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?

Respuesta :

Answer:

[tex]T = 4.48 s[/tex]

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

[tex]f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}[/tex]

so the time period of the oscillation is given as

[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]

so we will have

[tex]L = 5 m[/tex]

[tex]T = 2\pi\sqrt{\frac{5}{9.81}}[/tex]

[tex]T = 4.48 s[/tex]

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

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