Lesson summary
17.3.1 Damping — AS PHYSICS 9702 notes: Define damping and describe light, critical and heavy damping with their displacement–time graphs.Free oscillation — an ideal oscillator keeps its amplitude for ever, but real ones do notResistive forces — air resistance, viscous drag or fr…
- Continues until
- Energy and amplitude
- Resistive and restoring forces
- Exponential decay
- Definition
- Choosing a type
Section 1 of 10Energy loss in real oscillators
1Free oscillation
- Free oscillation an ideal oscillator keeps its amplitude for ever, but real ones do not
2Resistive forces
- Resistive forces air resistance, viscous drag or friction act against the motion, do work and transfer energy to the surroundings as thermal energy
3Damping
- Damping the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system
4Continues until
- Continues until the oscillator stops at the equilibrium position
5Energy and amplitude
- Energy and amplitude energy is proportional to amplitude squared, so halving the amplitude leaves a quarter of the energy
6Resistive and restoring forces
- Resistive and restoring forces the resistive force opposes motion and causes damping,
- whereas the restoring force returns the oscillator to equilibrium
Section 2 of 10Light damping
Behaviour
- Behaviour the object still oscillates but with decreasing amplitude, as a sine wave with progressively lower peaks
Envelope
- Envelope the peaks lie on a decaying curve
Exponential decay
- Exponential decay each cycle reduces the amplitude by the same fraction, not the same amount
Period
- Period almost unchanged, so the frequency is only very slightly lower than the natural frequency
Section 3 of 10Critical damping
Definition
- Definition just enough damping to return to equilibrium in the shortest possible time without oscillating
Graph
- Graph the displacement falls smoothly to zero without crossing the axis, with a steep initial gradient, then stays at x = 0
Examples
- Examples car suspension and moving-coil meters aim for close to critical damping
Section 4 of 10Heavy damping
Definition
- Definition damping greater than critical, so the object returns to equilibrium without oscillating but more slowly
Graph
- Graph no oscillations and the displacement creeps to zero after a long time, with a slow initial gradient
Section 5 of 10Comparing the types
| Damping | Behaviour |
|---|---|
| None | Constant-amplitude sinusoid |
| Light | Oscillates with exponentially decreasing amplitude |
| Critical | Fastest return to zero, no overshoot |
| Heavy | Slow return, no overshoot |
- Choosing a type
- musical instruments need very light damping so notes ring, and analogue meters and scales need critical damping so the needle settles quickly
Section 6 of 10Testing exponential decay
Method
- Method measure peak amplitudes A₁, A₂, A₃ and check that A₂/A₁ = A₃/A₂
Graph
- Graph ln A against the number of cycles is a straight line with negative gradient
Link
- Link the same exponential idea appears in capacitor discharge
Section 7 of 10Damping in practice
Useful damping
- Useful damping vehicle shock absorbers use fluid friction, and tall buildings in earthquake zones carry large damped masses
Resonance
- Resonance the heavier the damping, the smaller and broader the resonance peak
Timing a pendulum
- Timing a pendulum air resistance reduces the amplitude slowly but the period stays nearly the same, so the timing remains valid
Energy
- Energy the lost mechanical energy warms the surroundings and the damping material, in line with conservation of energy
Section 8 of 10More from the specification
More from the specification
Simple harmonic motion damping mechanisms
- Damping is the loss of mechanical energy from an oscillating system due to resistive frictional or viscous forces,
- causing amplitude to decrease over time.
Degrees of damping
- Light damping causes exponential decay of amplitude;
- critical damping returns the system to equilibrium in minimum time without oscillation;
- heavy damping causes sluggish return.
Resonance and forced oscillations
- When a periodic driving force matches the natural frequency of an oscillator, resonance occurs,
- resulting in maximum energy transfer and peak response amplitude.
Simple harmonic motion damping mechanisms
- Damping is the loss of mechanical energy from an oscillating system due to resistive frictional or viscous forces,
- causing amplitude to decrease over time.
Degrees of damping
- Light damping causes exponential decay of amplitude;
- critical damping returns the system to equilibrium in minimum time without oscillation;
- heavy damping causes sluggish return.
Resonance and forced oscillations
- When a periodic driving force matches the natural frequency of an oscillator, resonance occurs,
- resulting in maximum energy transfer and peak response amplitude.
Displacement-time graph
- A graph of displacement against time whose gradient is velocity.
Driving frequency
- The frequency of the periodic external force
Forced oscillation
- Oscillation caused by a periodic driving force
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Damping | reduction in energy and amplitude of oscillations due to resistive forces |
| Light damping | damping in which the oscillator keeps oscillating with decaying amplitude |
| Critical damping | damping giving the shortest return to equilibrium without oscillation |
| Heavy damping | damping greater than critical, giving a slow return without oscillation |
| Resistive force | a force opposing the motion, such as friction or air resistance |
| Exponential decay | decay in which equal fractions are lost in equal times |
Section 10 of 10Exam technique
1
Saying damping changes the frequency greatly — in light damping the period is almost unchanged.
2
Confusing resistive and restoring forces — resistive forces cause damping.
3
Saying the amplitude decreases linearly — it decays exponentially.
4
Saying critical damping oscillates — it returns without oscillating in the shortest time.