A particle of mass 1kg undergoes simple harmonic motion and its potential energy U changes with displacement x from a fixed point as shown below. Determine a) amplitude b) period
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To determine the amplitude and period of the simple harmonic motion from the given graph of potential energy U versus displacement x, you can follow these steps:
a) Amplitude:
The amplitude of simple harmonic motion is the maximum displacement of the particle from its equilibrium position. In the graph, the amplitude corresponds to the maximum value of the potential energy curve.
1. Identify the point(s) where the potential energy curve reaches its maximum value.
2. Determine the displacement value(s) corresponding to the maximum potential energy point(s).
3. The amplitude is equal to the absolute value of the displacement at any of these maximum points.
b) Period:
The period of simple harmonic motion is the time taken for the particle to complete one full vibration. In other words, it is the time taken for the particle to complete one full cycle.
1. Identify the distance between two consecutive points where the potential energy curve crosses the x-axis.
2. Determine the displacement values corresponding to these points.
3. The period is equal to the time taken to move from one of these points to the next and back to the initial point.
By following these steps and analyzing the given graph, you should be able to determine the amplitude and period of the simple harmonic motion.