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
Table 1
time/s          displacement(x)/m
0.00             0.980
2.00             -0.82
4.00              0.73
6.00             -0.60
8.00             0.53
10.0             -0.44
12.0             0.38


Question
What was the initial energy transferred to the child.
What was the length of the swing? (Treat the swing and the child as a single particle, and ignore the mass of the ropes that support the swing.
To the nearest second determine the time constant with which the amplitude of the oscillation decays
What was the approximate energy of the oscillator after 10 s?

Explanation / Answer

you can simply refer to the tagged topic and write down the equation of motion.

plug it into mathematica / mat lab, then you get the approximate value of b and k.

after getting these data, the questions are just a piece of cake.

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