A physicist takes his child to play on a swing. The total mass of the child and

Question

A physicist takes his child to play on a swing. The total mass of the child and the swing seat is 16.0 kg. The physicist pulls the swing (with the child sitting on it) back a distance of 0.980 m and releases it, so that the child swings to and fro. The physicist then produces a notebook, and makes a series of measurements of the maximum and minimum displacement of the swing from its equilibrium position during successive oscillations. The physicist also records the times of these maxima and minima. The results are as follows:

Later, the physicist uses these data to model the motion of the swing, treating it as a case of damped (horizontal) harmonic motion, with light damping. The motion can be considered to be lightly damped because the amplitude of the oscillations gradually decreases while the period remains constant.
Answer the following questions about this procedure, showing all your working at each step.

(a) What was the angular frequency of the child’s motion?

(b) What was the initial energy transferred to the child?

(c) To the nearest second determine the time constant with which the amplitude of the oscillation decays (you may want to use the graph provided in Figure 1).

(d)What was the approximate energy of the oscillator after 10 s?

Really need help answering all of these... thank you very much for any and all time time/ effort spent helping me.

Very best,

Miss Lightning.

Explanation / Answer

a) period T=4s so w=2pi/T=1.57(rad/s) b). initial energy. K=m*w^2*x0^2/2=19(J). c)we have that A=A0*e^(-t/T). take A=0.73 . A0=0.98 , t=4 (you can use other method for better accuracy but to make it simple, we can do this). ln(0.73/0.98)=-4/T so T=13.6(s) d) after 10s. A=0.44. so K=m*w^2*x0^2/2=3.8(J)

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