OscillationsEdexcel International A Level Physics: Topic test

20 questions, 54 marks

Edexcel International A Level Physics

Oscillations topic test

Total 54 marks

Name

Class

Date

1
A pendulum clock has a pendulum, which may be treated as a simple pendulum, with a period of 2.00 s on Earth, where g = 9.81 m s⁻² (9.81 N kg⁻¹).
(a)
What is the length of the pendulum?
[1 mark]
A3.12 m
B0.994 m
C0.101 m
D0.248 m
(b)
The clock is taken to the Moon, where g = 1.62 N kg⁻¹. What is the period of the same pendulum on the Moon?
[1 mark]
A0.81 s
B2.00 s
C4.92 s
D12.1 s
(c)
Explain why the motion of a simple pendulum is simple harmonic only for small amplitudes.
[2 marks]
Total for question 1: 4 marks
2
The cone of a loudspeaker moves with simple harmonic motion given by x = 2.0 × 10⁻³ cos(2π × 440 t), where x is in metres and t is in seconds.
(a)
What is the gradient of the displacement–time graph of the cone at t = 0?
[1 mark]
Azero
B5.5 m s⁻¹
C−5.5 m s⁻¹
D7.6 × 10⁶ m s⁻¹
(b)
What is the greatest gradient of the velocity–time graph of the cone?
[1 mark]
A5.5 m s⁻²
B7.6 × 10⁶ m s⁻²
C3.9 × 10² m s⁻²
D1.5 × 10⁴ m s⁻²
(c)
Calculate the time after t = 0 at which the cone first reaches its maximum speed, and the value of this maximum speed.
[2 marks]
Total for question 2: 4 marks
3
A block of mass 0.50 kg is attached to a light horizontal spring of spring constant 200 N m⁻¹ and rests on a table. The block is pulled 0.050 m from its equilibrium position and released from rest.
(a)
Assume that the table is frictionless. Calculate the speed of the block when its displacement from equilibrium is 0.030 m.
[3 marks]
(b)
In practice the table is rough, so the oscillations are damped, and after several oscillations the amplitude has fallen to 0.035 m. Calculate the energy dissipated, and state what happens to this energy.
[4 marks]
Total for question 3: 7 marks
4
A playground swing has chains that make it equivalent to a simple pendulum of length 2.5 m. A child of total mass 25 kg sits on the swing. Take g = 9.81 m s⁻² and assume the amplitude of the swing is small.
(a)
A parent pushes the child at regular intervals. Calculate the natural frequency of the swing, and explain how the parent should push to produce a large amplitude, why a push at a much higher frequency is ineffective, and the effect of friction at the pivots.
[6 marks]
(b)
The child swings with an amplitude of 0.50 m, measured along the arc, and the motion may be treated as simple harmonic. Calculate the maximum speed of the child, the maximum acceleration of the child, and the maximum kinetic energy of the child. After the parent stops pushing, the amplitude falls to 0.25 m. Calculate the energy dissipated.
[6 marks]
Total for question 4: 12 marks
5
Two identical tuning forks, X and Y, each of natural frequency 440 Hz, are mounted on separate resonance boxes a short distance apart. Fork X is struck and left to vibrate. Fork Y, initially at rest, gradually starts to vibrate in response to the sound from X. A third fork Z, of natural frequency 512 Hz, is placed at the same distance from X and shows only a very small response.
(a)
Which statement describes fork X after it has been struck and left to vibrate?
[1 mark]
AIt performs a forced oscillation at 440 Hz with a constant amplitude.
BIt performs a free oscillation at 440 Hz with a constant amplitude.
CIt performs a free oscillation at its natural frequency with a decreasing amplitude.
DIt performs a forced oscillation at the natural frequency of Y.
(b)
A piece of foam rubber is attached to fork Y to increase its damping. Which statement about the response of Y is correct?
[1 mark]
AThe amplitude at resonance is smaller and the peak is less sharp.
BThe amplitude at resonance is greater and the peak is sharper.
CThe amplitude at resonance is unchanged because the driving frequency is still 440 Hz.
DY no longer responds, because resonance only occurs for undamped systems.
(c)
State the frequency at which fork Z vibrates, and explain why the amplitude of its vibration is very small.
[2 marks]
Total for question 5: 4 marks
6
A vibration test table moves vertically with simple harmonic motion of amplitude 0.12 m and period 0.80 s. Its displacement x is given by x = 0.12 cos ωt, so that x = +0.12 m at t = 0.
(a)
What is the speed of the table at t = 0.20 s?
[1 mark]
Azero
B7.4 m s⁻¹
C0.15 m s⁻¹
D0.94 m s⁻¹
(b)
At which time in the first 0.80 s is the gradient of the velocity–time graph most negative?
[1 mark]
A0.20 s
B0 s
C0.40 s
D0.60 s
(c)
Calculate the speed of the table when its displacement is 0.060 m, on its way down from t = 0.
[2 marks]
Total for question 6: 4 marks
7
A car of mass 1200 kg, including passengers, is supported on four identical springs, each of spring constant 3.0 × 10⁴ N m⁻¹. After the car passes over a bump, the body of the car oscillates vertically as a single mass on the four springs, and the shock absorbers damp the motion.
(a)
Calculate the period of vertical oscillation of the body of the car.
[3 marks]
(b)
The amplitude of the first oscillation is 0.050 m and the amplitude of the third oscillation is 0.0125 m. Calculate the percentage of the vibrational energy that has been lost, and explain, in terms of energy, how the shock absorbers reduce the amplitude.
[4 marks]
Total for question 7: 7 marks
8
A footbridge has an effective vibrating mass of 1.2 × 10⁵ kg and a natural frequency of vertical vibration of 1.8 Hz. A crowd of people walks across it at about 110 steps per minute and the deck begins to bounce with a large amplitude. The bridge deck may be treated as a mass–spring oscillator.
(a)
Explain why the bridge deck oscillates with a large amplitude, and describe three ways in which engineers could reduce the amplitude of the oscillations.
[6 marks]
(b)
The deck bounces with an amplitude of 0.015 m. Calculate the effective spring constant of the bridge, the maximum energy of the oscillation, the maximum acceleration of the deck, and the energy of the oscillation if dampers reduce the amplitude to 0.0050 m.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).