How do damping and an external driving force change an oscillation, and why does resonance occur?
Describe free, damped and forced oscillations, distinguish light, critical and heavy damping, and explain resonance and its dependence on damping
A focused answer to the H2 Physics learning outcome on damping and resonance. Free versus forced oscillations, light, critical and heavy damping, and how resonance occurs when the driving frequency matches the natural frequency.
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What this dot point is asking
SEAB wants you to describe free, damped and forced oscillations, distinguish light, critical and heavy damping, and explain resonance, including how the resonance peak depends on the amount of damping. These ideas explain everything from why a pushed swing builds up to why a car suspension does not bounce.
The answer
Free oscillations
A free oscillation occurs when a system is displaced and released, then oscillates at its own natural frequency with no further external force. With no damping, the amplitude and energy stay constant. The natural frequency depends only on the system's properties (mass and stiffness for a spring, length and for a pendulum).
Damped oscillations
Real oscillations lose energy to resistive forces (friction, air resistance), so the amplitude decreases over time. This is damping. The degree of damping is classified by how the system returns to equilibrium:
- Light damping: the amplitude decays gradually over many oscillations (an exponential envelope).
- Critical damping: the system returns to equilibrium in the shortest possible time without oscillating.
- Heavy (over) damping: the system returns to equilibrium slowly without oscillating, taking longer than critical damping.
Critical damping is the boundary case and is the design target for instruments and suspensions that must settle quickly.
Forced oscillations
If an external periodic force drives a system, the system performs forced oscillations. After an initial transient, it oscillates at the driving frequency (not its own natural frequency), with an amplitude that depends on how close the driving frequency is to the natural frequency.
Resonance
Resonance occurs when the driving frequency equals (or is very close to) the system's natural frequency. At resonance:
- the system absorbs energy from the driver most efficiently,
- the amplitude of the forced oscillation reaches a maximum.
The shape of the resonance curve (amplitude against driving frequency) depends on damping:
- light damping gives a tall, sharp peak at a frequency very close to ,
- heavier damping gives a shorter, broader peak shifted slightly below .
Examples in context
Example 1. Tuning a radio. A radio receiver has a circuit whose natural frequency is adjusted to match the broadcast frequency. At resonance the circuit responds strongly to that station and weakly to others, which is how a single station is selected from many. This is resonance used deliberately and constructively.
Example 2. The Tacoma Narrows bridge. Wind produced a periodic driving force near the bridge's natural frequency, and with too little damping the oscillation amplitude grew until the structure failed. Modern bridges add damping and stiffening to shift natural frequencies away from likely driving frequencies, the destructive side of resonance.
Try this
Q1. State the condition for resonance to occur. [1 mark]
- Cue. The driving frequency equals (or is very close to) the natural frequency of the system.
Q2. Describe the difference between critical damping and light damping in terms of how a displaced system returns to equilibrium. [2 marks]
- Cue. Critical damping returns in the shortest time without oscillating; light damping oscillates with gradually decreasing amplitude.
Q3. Explain how increasing the damping of a system changes its resonance curve. [3 marks]
- Cue. The peak becomes lower and broader, the maximum amplitude falls, and the peak shifts slightly to a frequency below the natural frequency.
Exam-style practice questions
Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Original5 marks(a) Distinguish between free and forced oscillations. (b) Explain what is meant by resonance, and describe how the amplitude at resonance depends on the degree of damping.Show worked answer →
(a) A free oscillation occurs at the system's natural frequency with no external periodic force after the initial displacement (energy is constant if undamped). A forced oscillation is driven by an external periodic force, and the system eventually oscillates at the driving frequency.
(b) Resonance occurs when the driving frequency equals (or is very close to) the natural frequency of the system. At resonance the system absorbs energy most efficiently and the amplitude reaches a maximum.
The amplitude at resonance depends on damping: lighter damping gives a larger, sharper resonance peak at a frequency close to the natural frequency; heavier damping gives a smaller, broader peak shifted slightly to a lower frequency.
Markers reward the free-versus-forced distinction (natural versus driving frequency), the resonance condition (driving frequency near natural frequency), and the effect of damping on the height and sharpness of the peak.
Original4 marksA car suspension uses dampers. (a) Explain why critical damping is desirable for a car suspension. (b) Describe what would happen to the ride if the dampers were worn so the system became lightly damped.Show worked answer →
(a) Critical damping returns the system to equilibrium in the shortest time without oscillating. For a suspension this means the car settles quickly after a bump without bouncing, giving a controlled, comfortable ride.
(b) With worn dampers the system becomes lightly damped, so after a bump the car would oscillate up and down several times before settling. The ride would feel bouncy and the wheels could lose contact with the road, reducing control and safety.
Markers reward critical damping as the fastest non-oscillatory return, and the description of light damping producing prolonged unwanted oscillation after a disturbance.
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