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PERIODIC MOTION - Coggle Diagram
PERIODIC MOTION
The Simple Pendulum
A simple pendulum consists of a mass at the end of a lightweight cord. We assume that the cord does not stretch, and that its mass is negligible.
In order to be in SHM, the restoring force must be proportional to the negative of the displacement.
which is proportional to sin θ and not to θ itself.
However, if the angle is small, sin θ ≈ θ.
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where x = 0
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So, as long as the cord can be considered massless and the amplitude is small, the period does not depend on the mass.
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Damped Harmonic Motion
Damped harmonic motion is harmonic motion with a frictional or drag force. If the damping is small, we can treat it as an “envelope” that modifies the undamped oscillation.
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Oscillations of a Spring
If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a useful model for a periodic system.
We assume that the surface is frictionless. There is a point where the spring is neither stretched nor compressed; this is the equilibrium position. We measure displacement from that point (x = 0 on the previous figure).
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If the spring is hung vertically, the only change is in the equilibrium position, which is at the point where the spring force equals the gravitational force.
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