Results
The next figure shows the position vs time graph of the two balls. The position was measured using the procedure in the previous page, while the time was obtained using knowledge of the frame rate of the camera (59 fps, to be exact). Furthermore, the position was converted from pixel units to meters using a conversion factor of 0.000669, obtained using the ruler placed inside the frame.
Notice that when the red-marked golf ball has high-amplitude oscillation, the blue-marked ball has low-amplitude oscillation, and vice versa. It’s as if energy is being transferred from one ball to the other in an alternating manner, possible evidence that energy is being conserved in the whole system. Next, we look at the velocity of both golf balls.
There is a similar trend wherein when one ball has high velocity the other one has low velocity, as they transfer energy between them. Since energy is computed using KE = 0.5mv^2, and assuming that the mass of both balls is the same, getting the summation of velocity squared is enough to approximate energy. However, it is important to note here that the velocity is a rapidly varying function, and hence a time-averaged summation is necessary. Below is the result when a time-averaged summation over ~0.25 s of the squared velocity is obtained.
While the approximation for energy is oscillating, note that it oscillates about 0.16 while gradually decreasing overall. The general decrease is due to the damping force of air and friction inside the system (between strings and supports). Also, the oscillating behaviour is attributed to the rapidly varying velocity and the relatively small averaging window.
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