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Oscillations (Damping (Critical Damping (Reduces amplitude in shortest…
Oscillations
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Simple Harmonic Motion
Periodic motion in which the acceleration of the particle is directly proportional to its displacement from, and always towards, a fixed point
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Restoring Force
Always restoring force that which pulls or pushes object back towards midpoint, causing it to accelerate in that direction - size depends on displacement
Object will move with SHM if restoring force directly proportional to objects displacement from the midpoint, in the opposite direction to the displacement
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Frequency and amplitude independent of amplitude - constant for a fixed oscillation - pendulum clock will always tick in regular time intervals even if swing becomes very small
Resonance
Occurs when natural frequency of oscillations matches the driving frequency of forced oscillations (for undamped oscillators)
As driving frequency approaches natural frequency, system gains more energy from driving force so oscillates with rapidly increasing amplitude
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Resonance Peaks
Lightly damped systems have sharp resonance peak - amplitude increases dramatically when driving frequency very close to natural frequency
Heavily damped systems give flatter response- amplitude doesn't increase very much near natural frequency and isn't as sensitive to driving frequency
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Types of oscillations
Free Oscillations
- No external forces acting on the body
- No energy transferred to or from the surroundings
- keeps oscillating with the same amplitude forever at the natural frequency according to principle of conservation of energy
Free Damped Oscillations
- Energy lost from oscillating system due to frictional forces
- Amplitude becomes progressively smaller
- Damping can be natural or artificial
Forced Oscillations
- Energy put into the system to make it vibrate at a frequency that is not the natural frequency
