Forced Vibrations & Resonance

Damping types, free and forced oscillations, resonance curves, and the effects of damping on resonance.

Spec Points Covered
  • Define dampingThe reduction in amplitude (and energyThe capacity to do work. Measured in joules (J).) of an oscillation over time due to resistive forces such as friction or air resistance. and describe the three types: light, critical, and heavy.
  • Distinguish between free and forced oscillations.
  • Define resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energyThe capacity to do work. Measured in joules (J). transfer. and identify it on a frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).-amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). graph.
  • Describe how dampingThe reduction in amplitude (and energyThe capacity to do work. Measured in joules (J).) of an oscillation over time due to resistive forces such as friction or air resistance. affects the resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energy transfer. curve.
  • Give real-world examples of resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energy transfer. and dampingThe reduction in amplitude (and energy) of an oscillation over time due to resistive forces such as friction or air resistance..
Notes
01 Damping is the loss of energy from an oscillating system Damping 3.6.1.4 → 02 Light damping: amplitude decays exponentially over many oscillations Light damping 3.6.1.4 → 03 Critical damping returns to equilibrium in the shortest time without oscillating Critical damping 3.6.1.4 → 04 Heavy damping returns to equilibrium slowly without oscillating Heavy damping 3.6.1.4 → 05 Free oscillations have no energy input; forced oscillations are driven externally Free oscillation 3.6.1.4 → 06 Resonance occurs when the driving frequency equals the natural frequency Natural frequency 3.6.1.4 → 07 The resonance curve shows amplitude peaking at the natural frequency 3.6.1.4 → 08 Resonance has useful and destructive applications 3.6.1.4 →
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Q Retrieval Practice All 11 Questions →
Q1. Define damping.
The reduction in energy and amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). of oscillations due to resistive forces acting on the oscillating system.
Q2. Name the three types of damping and give one example of each.
  • Light damping: swinging pendulum in air.
  • Critical damping: car suspension.
  • Heavy damping: door closer mechanism.
Q3. What happens to the frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of oscillation as a lightly damped system loses amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m).?
  • The frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). stays the same.
  • Only the amplitude decreases.
  • The time periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). remains constant.
Q4. Define critical damping.
The degree of damping where the system returns to equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. in the shortest possible time without any oscillation.
Q5. Distinguish between free and forced oscillations.
  • Free: only internal forces, no energy input, oscillates at natural frequencyThe frequency at which a system oscillates freely when displaced from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. and released, with no external driving force..
  • Forced: periodic external driving force, energy input, oscillates at the driving frequency.