A Level Physics 17.3 Damped and Forced Oscillations, Resonance MCQs – 30 Practice Questions with Answers (Cambridge 9702)
These 30 original practice MCQs cover Section 17.3, Damped and Forced Oscillations, Resonance, of the Cambridge International AS & A Level Physics (9702) syllabus. This is an A Level (A2) topic: it explains why real oscillations die away, how a system responds to a periodic driving force, and why the amplitude becomes very large at resonance.
Key ideas recap: in light damping the amplitude decreases approximately exponentially while the period stays almost unchanged; critical damping gives the fastest return to equilibrium without overshooting. A forced oscillator oscillates at the driving frequency, and resonance (maximum amplitude) occurs when the driving frequency equals the natural frequency f0, with the displacement lagging the driving force by π/2 rad (90°) at resonance. See the full A Level Physics Formula Sheet for the oscillation equations used in this topic.
Damping
Q1. Damping of an oscillation means that
- (A) the frequency of the oscillation gradually decreases
- (B) the amplitude decreases because energy is transferred away from the oscillator by resistive forces
- (C) the mass of the oscillator gradually decreases
- (D) the period increases until the oscillation stops completely
Show Answer
Answer: B – Resistive forces such as friction and air resistance do work against the motion, so energy leaves the oscillating system (mainly as thermal energy) and the amplitude falls.
Q2. For a lightly damped oscillator, the amplitude of the oscillations
- (A) decreases approximately exponentially with time
- (B) decreases by the same amount in each cycle
- (C) stays constant and then suddenly drops to zero
- (D) increases for a few cycles and then decreases
Show Answer
Answer: A – With light damping the fraction of energy lost per cycle is roughly constant, so each successive peak is a fixed fraction of the one before: an approximately exponential decay. The oscillation continues for many cycles.
Q3. Light damping has what effect on the period of an oscillator?
- (A) The period doubles
- (B) The period decreases rapidly
- (C) The period is almost unchanged
- (D) The period becomes zero
Show Answer
Answer: C – Light damping removes energy and reduces the amplitude, but the oscillator still swings at close to its natural frequency, so the period is only very slightly affected.
Q4. A heavily (over-) damped system, such as a mass on a spring in thick oil, is displaced and released. It
- (A) oscillates with a slowly decreasing amplitude
- (B) oscillates with a rapidly increasing amplitude
- (C) returns to equilibrium and overshoots several times
- (D) creeps back to equilibrium without oscillating
Show Answer
Answer: D – With heavy damping the resistive forces are so large that the system cannot complete even one oscillation; it returns to the equilibrium position slowly, from whichever side it was released.
Q5. Critical damping is the condition in which the system
- (A) returns to equilibrium in the shortest possible time without overshooting
- (B) oscillates once and then stops
- (C) takes the longest possible time to return to equilibrium
- (D) keeps oscillating with constant amplitude
Show Answer
Answer: A – Critical damping is the boundary between oscillating (light damping) and creeping back (heavy damping): the system settles at equilibrium as fast as possible, with no overshoot.
Q6. The energy lost by a damped oscillator is mainly transferred to
- (A) the kinetic energy of the oscillator
- (B) the thermal (internal) energy of the oscillator and its surroundings
- (C) the gravitational potential energy of the oscillator
- (D) sound energy only
Show Answer
Answer: B – Work is done against friction and air resistance, so the mechanical energy of the oscillator is converted into thermal energy. This is why a damped oscillator and its surroundings warm up very slightly.
Q7. The dampers (shock absorbers) in a car suspension are designed to give close to critical damping so that, after a bump,
- (A) the car body keeps bouncing for as long as possible
- (B) the wheels leave the road surface
- (C) the car body returns quickly to its normal position without repeated bouncing
- (D) the springs store more energy
Show Answer
Answer: C – Near-critical damping lets the wheel follow the road and settle almost immediately. Too little damping would leave the car bouncing; too much would make the ride harsh and slow to respond.
Q8. The pointer of an analogue ammeter is designed to be critically damped so that it
- (A) swings past the reading several times before stopping
- (B) takes a very long time to reach the reading
- (C) stays at zero until the current is large
- (D) moves quickly to the correct reading and stays there without oscillating
Show Answer
Answer: D – Critical damping brings the pointer to rest at the measured value in the shortest time, which makes the meter quick and easy to read.
Q9. A pendulum swings first in air and then immersed in oil. Compared with air, in the oil
- (A) the amplitude decreases much more rapidly because the resistive forces are greater
- (B) the amplitude stays the same for longer
- (C) the pendulum oscillates at a much higher frequency
- (D) there is no damping at all
Show Answer
Answer: A – The viscous drag in oil is far greater than air resistance, so energy is removed much faster per swing and the oscillations die away quickly – the system is much more heavily damped.
Q10. Which description fits a lightly damped oscillator?
- (A) It returns to equilibrium without oscillating
- (B) It oscillates for many cycles while its amplitude gradually decreases
- (C) It oscillates with constant amplitude forever
- (D) It stops after exactly one complete oscillation
Show Answer
Answer: B – Light damping removes only a small fraction of the energy in each cycle, so the system keeps oscillating for a long time with a slowly shrinking amplitude.
Forced Oscillations & Resonance
Q11. A system oscillating freely, with no driving force and negligible damping, oscillates at
- (A) zero frequency
- (B) the frequency of the last force applied to it
- (C) its natural frequency, which is fixed by the properties of the system itself
- (D) a frequency that increases steadily with time
Show Answer
Answer: C – In free oscillation the frequency is the natural frequency of the system – for example, it depends on the mass and the spring constant for a mass-spring system.
Q12. When a system is forced to oscillate by a periodic external force, after any starting effects have died away it oscillates at
- (A) the frequency of the driving force
- (B) its own natural frequency only
- (C) twice its natural frequency
- (D) a frequency halfway between the driving and natural frequencies
Show Answer
Answer: A – In a forced oscillation the system is driven: it settles down to oscillate at the driving frequency. Its natural frequency still matters, because it controls how big the amplitude is at that driving frequency.
Q13. Resonance occurs when
- (A) the driving frequency is much greater than the natural frequency
- (B) the driving force is switched off
- (C) the amplitude of the oscillator is zero
- (D) the driving frequency is equal to the natural frequency of the system
Show Answer
Answer: D – At this driving frequency the force feeds energy into the system most effectively, in time with its motion, so the amplitude builds up to a maximum limited only by the damping.
Q14. The amplitude is greatest at resonance because
- (A) the driving force becomes larger at that frequency
- (B) the driving force is in phase with the velocity of the oscillator, so energy is transferred to it at the maximum rate
- (C) damping disappears completely at resonance
- (D) the mass of the oscillator changes
Show Answer
Answer: B – At resonance the applied force is always in the same direction as the motion, doing positive work throughout each cycle. Energy is transferred in at the greatest possible rate, balancing the losses at a large amplitude.
Q15. At resonance, the phase difference between the driving force and the displacement of the oscillator is
- (A) zero – they are exactly in phase
- (B) π rad (180°) – they are in antiphase
- (C) π/2 rad (90°) – the displacement lags the driving force by π/2 rad
- (D) it changes randomly from cycle to cycle
Show Answer
Answer: C – At resonance the driving force is 90° (π/2 rad) ahead of the displacement, which means it is exactly in phase with the velocity – the condition for maximum energy transfer.
Q16. On a graph of amplitude against driving frequency, reducing the damping makes the resonance peak
- (A) higher and sharper (narrower)
- (B) lower and broader
- (C) disappear completely
- (D) move to zero frequency
Show Answer
Answer: A – With less damping, less energy is lost per cycle, so the amplitude grows larger, and the response is large only very close to the natural frequency: a tall, narrow, sharp peak.
Q17. A heavily damped system shows a resonance curve in which the peak is
- (A) extremely tall and narrow
- (B) at exactly zero frequency
- (C) identical to the undamped curve
- (D) low and flat (broad), with maximum amplitude much reduced
Show Answer
Answer: D – Heavy damping removes energy quickly, so the amplitude can never build up much, whatever the driving frequency. The response changes only slowly with frequency, giving a low, broad curve.
Q18. The natural frequency of a mass-spring oscillator is determined by
- (A) the amplitude of the oscillations
- (B) the mass and the spring constant (stiffness) of the spring
- (C) the size of the driving force
- (D) the amount of damping present
Show Answer
Answer: B – The natural frequency depends only on the system itself: a larger mass lowers it and a stiffer spring raises it. The amplitude and the driver do not set the natural frequency.
Q19. At resonance, the velocity of the oscillator is
- (A) in antiphase with the driving force
- (B) in phase with the driving force
- (C) always zero
- (D) at right angles to the driving force in space
Show Answer
Answer: B – Power transferred equals force × velocity, so the transfer is greatest when force and velocity are in phase, which is exactly the situation at resonance (the displacement is π/2 rad behind both).
Q20. When the driving frequency is far below the natural frequency, the displacement of the oscillator is
- (A) almost in phase with the driving force, following it slowly
- (B) in antiphase with the driving force
- (C) exactly zero
- (D) lagging the force by π/2 rad
Show Answer
Answer: A – Driven slowly, the system simply follows the force almost as if it were static, so the displacement is nearly in phase with the force. The π/2 rad lag occurs at resonance, and antiphase occurs well above resonance.
Resonance in Practice
Q21. In the Barton’s pendulums demonstration, several pendulums of different lengths hang from the same string as a heavy driver pendulum. The pendulum that swings with by far the largest amplitude is the one
- (A) with the shortest string
- (B) with the longest string
- (C) with the heaviest bob
- (D) with the same length as the driver pendulum
Show Answer
Answer: D – A pendulum’s natural frequency depends on its length. The pendulum matching the driver has the same natural frequency as the driving frequency, so it resonates and builds up a large amplitude.
Q22. In Barton’s pendulums, the matching pendulum responds so strongly because
- (A) it receives the largest pushes from the string
- (B) it has no damping
- (C) its natural frequency is equal to the frequency of the driving force
- (D) its bob is attracted to the driver bob
Show Answer
Answer: C – All the pendulums receive similar small pushes through the string, but only the one whose natural frequency matches the driving frequency is in resonance, so only it accumulates energy cycle after cycle.
Q23. Soldiers are ordered to break step when marching across a bridge in order to
- (A) avoid driving the bridge at its natural frequency and building up dangerously large oscillations
- (B) reduce the total weight on the bridge
- (C) make the bridge oscillate more strongly
- (D) increase the natural frequency of the bridge
Show Answer
Answer: A – Marching in step applies a periodic force at one frequency. If that matches the bridge’s natural frequency, resonance can make the bridge’s oscillations grow to a dangerous size; breaking step removes the steady driving frequency.
Q24. In a microwave oven, the frequency of the microwaves is chosen so that water molecules in the food
- (A) are broken apart by the radiation
- (B) stop rotating completely
- (C) absorb energy strongly, being driven to vibrate and rotate at a frequency they respond to most, heating the food
- (D) reflect all the microwaves away
Show Answer
Answer: C – The oscillating electric field of the microwaves drives the water molecules at a frequency they absorb very efficiently, so their rotational and vibrational energy increases rapidly – a resonance-like transfer of energy that cooks the food.
Q25. Tuning a radio receiver to a particular station works by
- (A) increasing the damping of the aerial until only one station is heard
- (B) adjusting the natural frequency of the receiver circuit to match the frequency of the wanted station’s carrier wave
- (C) making the aerial longer than every wavelength
- (D) removing all resonance from the circuit
Show Answer
Answer: B – The receiver circuit resonates at one frequency only. Setting its natural frequency equal to the station’s frequency gives a large response to that station, while signals at other frequencies produce only a tiny response.
Q26. During an earthquake, the buildings most at risk of very large oscillations are those for which
- (A) the foundations are made of the hardest rock
- (B) the building is the tallest in the city
- (C) damping in the structure is greatest
- (D) the natural frequency of the building matches the frequency of the ground oscillations
Show Answer
Answer: D – The shaking ground is a driving force. A building whose natural frequency matches the driving frequency resonates, so its sway builds up to a large and possibly destructive amplitude.
Q27. Engineers can reduce the danger of harmful resonance in a structure by
- (A) adding damping and/or changing the natural frequency of the structure
- (B) making the structure as light as possible
- (C) removing all damping from the structure
- (D) driving the structure harder so it passes resonance quickly
Show Answer
Answer: A – Extra damping limits the amplitude that can build up, and redesigning the stiffness or mass moves the natural frequency away from the driving frequency, so resonance no longer occurs.
Q28. A washing machine vibrates violently at one particular spin speed but is fairly quiet at lower and higher speeds. This is because
- (A) the drum is unbalanced at all speeds
- (B) the motor produces no force at other speeds
- (C) at that speed the frequency of the rotating out-of-balance force equals the natural frequency of the machine on its supports, so resonance occurs
- (D) damping is absent only at that speed
Show Answer
Answer: C – As the drum speeds up it passes through the resonant frequency of the machine-and-mounts system. Near that speed the amplitude is large; above it the response falls again.
Q29. If a car’s shock absorbers wear out, the car body bounces repeatedly after a bump. This happens because
- (A) the springs have become stiffer
- (B) the natural frequency of the body has become zero
- (C) there is now too little damping, so the oscillations of the body on its springs die away only slowly
- (D) resonance with the engine becomes stronger
Show Answer
Answer: C – The springs still support the car and set the natural frequency, but worn dampers remove very little energy per cycle. The result is a lightly damped system that keeps bouncing.
Q30. The air column inside a wind instrument, such as a flute or clarinet, produces a loud note because
- (A) the air is compressed to a very high pressure
- (B) the walls of the instrument vibrate instead of the air
- (C) damping inside the tube is at its maximum
- (D) the air resonates at its natural frequencies, building up a large-amplitude standing oscillation that radiates a strong sound
Show Answer
Answer: D – The player’s input drives the air column at one of its natural frequencies. Resonance builds up a large standing-wave oscillation in the tube, which is why a small input produces a loud, clear note.
Keep practising: revise the whole topic on the Physics MCQs hub and keep the key equations beside you with the A Level Physics Formula Sheet.
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