Swings and resonance: You are pushing a child on a swing, which is attached to r

Question

Swings and resonance:

You are pushing a child on a swing, which is attached to ropes that are 5 meters long. You are pushing periodically. if you choose the time interval between pushes correctly, the swing will have the highest amplitude for fixed magnitude of the pushing force.

a) How many seconds apart should you time your pushes? (That is, what is the optimal period for pushing?)

b) You decide to experiment with trying slightly different periodicities of pushing, and find that if you vary the optimal period by ±1sec, then the amplitude of the swing is still respectable. Estimate the damping coefficient .

suggestion: For part (b), you can start by showing that small changes in the period and the frequency are related by / = T/T Then use what you know about the frequency width of a damped, forced, oscillator.

Explanation / Answer

part a

time of pushing=time peroid

T=2*pi*(L/g)^0.5

T=2*3.1428*(5/9.81)^0.5

T=4.48742second

for part B

damped oscillaion we need mass of child

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