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So far we have studied idealised SHM — oscillations that continue forever with constant amplitude. In the real world, every oscillating system loses energy to its surroundings through friction, air resistance, or other dissipative forces. This causes the amplitude to decrease over time, a phenomenon called damping.
Before studying damping, it is important to distinguish two types of oscillation:
Free oscillations occur when a system is displaced from equilibrium and then left to oscillate without any external driving force. The system oscillates at its natural frequency f₀, which depends only on the system's physical properties (mass, spring constant, length, etc.). A pendulum set swinging and left alone is undergoing free oscillation.
Forced oscillations occur when an external periodic force continuously drives the system. The system oscillates at the driving frequency f_d, which may or may not equal the natural frequency. A child being pushed on a swing is an example of forced oscillation.
Damping occurs when resistive forces act on the oscillating system, removing energy with each cycle. Common sources include:
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