Oscillations: A Level Physics questions with answers
Free Oscillations questions for A Level Physics (9702), part of Fields & motion. Each question has the answer and the marking points an examiner would look for.
A pendulum is set oscillating with an amplitude of 6.0 cm. After 20 oscillations the amplitude has fallen to 3.0 cm.
(a)
State what is meant by damping.
[1]
(b)
Calculate the fraction of the original energy remaining after 20 oscillations.
[2]
(c)
Distinguish between light, critical and heavy damping.
[3]
(d)
State one useful example and one problem caused by resonance.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
loss of energy, amplitude decreases
energy is lost to the surroundings so the amplitude decreases B1
1
(b)
1/4
energy ∝ amplitude2C1 fraction = 1/4 A1
2
(c)
light: many oscillations; critical: returns fastest; heavy: slow return
light: oscillations with gradually decreasing amplitude B1 critical: returns to equilibrium in the shortest time without oscillating B1 heavy: returns slowly without oscillating B1
3
(d)
e.g. microwave oven / MRI; bridges, buildings
useful: e.g. microwave cooking, MRI, tuning a radio B1 problem: e.g. collapse of bridges, vibration of machinery B1
2
Question 2Structured · 9 marksA* challenge
A mass of 0.2 kg on a spring of spring constant 40 N m−1 oscillates vertically with simple harmonic motion of amplitude 8 cm.
(a)
Define simple harmonic motion.
[2]
(b)
Calculate the angular frequency and the period.
[2]
(c)
Calculate the maximum speed and the speed when the displacement is half the amplitude.
[3]
(d)
The oscillation is now lightly damped. Describe the effect on the amplitude and on the period.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
acceleration proportional to displacement from a fixed point and directed towards that point
acceleration ∝ displacement B1 directed towards the equilibrium point / opposite to displacement B1
2
(b)
14.1 rad s−1, 0.444 s
ω = √(k/m) C1 both correct A1
2
(c)
1.13, 0.98 m s−1
v0 = ωA C1 1.13 A1 0.98 A1
3
(d)
amplitude decreases gradually (exponentially); period almost unchanged
amplitude decreases B1 period (approximately) unchanged B1
2
Question 3Structured · 11 marks
A mass of 0.20 kg on a spring of spring constant 40 N m−1 oscillates vertically with amplitude 3.0 cm, performing simple harmonic motion.
(a)
State the defining equation of simple harmonic motion and explain the significance of the minus sign.
[2]
(b)
Show that the angular frequency ω = √(k/m), and calculate the frequency of the oscillations.
[3]
(c)
Calculate the maximum speed of the mass.
[2]
(d)
Calculate the total energy of the oscillations.
[2]
(e)
Calculate the speed of the mass when its displacement is 1.5 cm from equilibrium.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
a = −ω²x; acceleration directed towards equilibrium, opposite to displacement
a = −ω2x B1 the acceleration is always directed towards the equilibrium position / opposite to the displacement B1
2
(b)
2.25 Hz
a = −(k/m)x compared with a = −ω2x, so ω2 = k/m B1 ω = √(40/0.20) = 14.1 rad s−1C1 f = 2.25 Hz A1
3
(c)
0.424 m s−1
v0 = ωx0C1 0.424 m s−1A1
2
(d)
0.018 J
E = ½mω2x02C1 0.018 J A1
2
(e)
0.367 m s−1
v = ω√(x02 − x2) C1 0.367 m s−1A1
2
Question 4Structured · 12 marks
A car suspension is modelled as a mass on a spring with damping. The car body oscillates when it drives over a bump.
(a)
Distinguish between free and forced oscillations.
[2]
(b)
Describe what is meant by critical damping and explain why it is used in car suspensions.
[3]
(c)
The road has bumps every 15 m. The natural frequency of the suspension is 1.2 Hz. Calculate the speed of the car at which resonance occurs.
[2]
(d)
Sketch a graph of amplitude against driving frequency for light and heavy damping on the same axes.
Fig. 4.1
[3]
(e)
Give one useful application of resonance and one situation where resonance must be avoided.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
free: no external periodic force, natural frequency; forced: driven by periodic external force
free oscillations occur at the natural frequency with no external periodic force B1 forced oscillations are driven by an external periodic force at its frequency B1
2
(b)
returns to equilibrium in shortest time without oscillating; comfort and control
critical damping returns the system to equilibrium in the shortest possible time B1 without oscillating B1 so the car does not bounce repeatedly after a bump B1
3
(c)
18 m s−1
driving frequency = v/15 = 1.2 C1 v = 18 m s−1A1
2
(d)
both peak near natural frequency; heavy damping lower, broader, peak shifted lower
both curves rise to a peak near the natural frequency B1 heavily damped curve has a lower and broader peak B1 peak at a slightly lower frequency B1
useful: e.g. tuning a radio / MRI / microwave cooking B1 avoided: e.g. bridges in wind / buildings in earthquakes / machinery vibrations B1
2
Question 5Structured · 3 marks
An object oscillates with simple harmonic motion of frequency 2.2 Hz and amplitude 3.4 cm. Calculate its maximum speed.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.47 m s−1
ω = 2πf C1 vmax = ωx0C1 0.47 A1
3
Question 6Structured · 9 marks
A simple pendulum of length 0.50 m swings with small amplitude 6.0 cm. Its angular frequency is given by ω = √(g/L).
(a)
State the conditions for simple harmonic motion.
[2]
(b)
Calculate the period of the pendulum.
[2]
(c)
Calculate the maximum acceleration of the bob.
[2]
(d)
Sketch graphs of displacement and velocity against time on the same axes for one period, starting at maximum displacement.
Fig. 6.1
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
acceleration proportional to displacement; directed towards equilibrium
acceleration is proportional to displacement from a fixed point B1 and always directed towards that point (opposite to displacement) B1
2
(b)
1.42 s
ω = √(9.81/0.50) = 4.43 rad s−1C1 T = 1.42 s A1
2
(c)
1.18 m s−2
amax = ω2x0C1 1.18 m s−2A1
2
(d)
displacement cosine from +x0; velocity −sine, quarter period out of phase
displacement is a cosine curve starting at +x0B1 velocity is a negative sine curve with maximum ωx0B1 velocity is π/2 out of phase with displacement B1
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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in