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course PHY 201
10/07 8:10pm
A pendulum requires 2 seconds to complete a cycle, which consists of a complete back-and-forth oscillation (extreme point to equilibrium to opposite extreme point back to equilibrium and finally to the original extreme point). As long as the amplitude of the motion (the amplitude is the distance from the equilibrium position to the extreme point) is small compared to the length of the pendulum, the time required for a cycle is independent of the amplitude.·How long does it take to get from one extreme point to the other, how long from an extreme point to equilibrium, and how long to go from extreme point to equilibrium to opposite extreme point and back to equilibrium?
From 1 extreme point to the other takes just a little over 1 second, maybe 1.1 seconds.
From 1 extreme point back to equilibrium takes .55 seconds
From 1 extreme point to equilibrium to opposite extreme point and back to equilibrium should take 1.65 seconds
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answer/question/discussion:
· What reasonable assumption did you make to arrive at your answers?
To get to the 1st extreme point and back in order to complete 1 cycle of oscillation, the pendulum won’t travel the same distance. The pendulum does not have as much kinetic energy to make it back the same distance as when it was released (bowling ball example). So, since it won’t be traveling as far from the extreme point back to the origin because of a loss of kinetic energy, it should take the pendulum a tad bit longer to get to that 1st extreme point than from the extreme point back to the origin.
To get the time from the 1st extreme point back to equilibrium, I just took half of the time I thought it would take to get from 1 extreme point to the opposite extreme point.
To get the time from 1 extreme point to equilibrium to opposite extreme point and back to equilibrium, I added the 2 times 1.1s and .55s which I figured above.
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Close. But the period would in fact be expected to divide into four equal parts, each lasting .50 seconds, rather than .55 seconds. Your result would leave only .35 seconds to get from the opposite extreme point back to equilibrium, and there is no reason to expect that time to be shorter than the others.
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