OscillationsEdexcel A-Level Physics: Topic test

20 questions, 54 marks

Edexcel A-Level Physics

Oscillations topic test

Total 54 marks

Name

Class

Date

1
A buoy bobs vertically in the sea with simple harmonic motion of amplitude 0.40 m and period 5.0 s.
(a)
What is the angular frequency of the buoy's motion?
[1 mark]
A0.20 rad s⁻¹
B0.63 rad s⁻¹
C1.3 rad s⁻¹
D31 rad s⁻¹
(b)
What is the maximum speed of the buoy?
[1 mark]
A0.50 m s⁻¹
B0.080 m s⁻¹
C0.63 m s⁻¹
D2.0 m s⁻¹
(c)
Calculate the maximum acceleration of the buoy.
[2 marks]
Total for question 1: 4 marks
2
A simple pendulum of length 0.994 m is used in a clock on Earth, where g = 9.81 N kg⁻¹. The oscillations are small.
(a)
What is the period of the pendulum?
[1 mark]
A0.318 s
B2.00 s
C6.26 s
D1.00 s
(b)
By what factor must the length of the pendulum be increased to double the period?
[1 mark]
A2
B8
C1.4
D4
(c)
The clock is taken to the Moon, where g = 1.62 N kg⁻¹. Calculate the period of the pendulum on the Moon.
[2 marks]
Total for question 2: 4 marks
3
A mass on a spring oscillates with simple harmonic motion with an amplitude of 0.075 m and a period of 1.2 s. Its displacement from the equilibrium position is a cosine curve against time, with the maximum positive displacement at t = 0.
(a)
Calculate the maximum speed of the mass.
[3 marks]
(b)
Describe the velocity–time graph for the first complete oscillation, giving the times at which the velocity is zero and the times at which it has its greatest magnitude, with its values. Explain how this follows from the displacement–time graph.
[4 marks]
Total for question 3: 7 marks
4
A footbridge has a natural frequency of vertical oscillation of 1.9 Hz. On its opening day, many people walk across it at about 1.9 steps per second and the bridge oscillates with a large amplitude. Engineers later fit dampers to the bridge.
(a)
Explain why the bridge oscillated with a large amplitude on opening day, and describe and explain the effect of the dampers on the amplitude.
[6 marks]
(b)
Before the dampers were fitted, the middle of the bridge moved with simple harmonic motion at 1.9 Hz with an amplitude of 0.030 m. The oscillating part has an effective mass of 4.0 × 10⁴ kg. Calculate the maximum speed, the maximum kinetic energy, the maximum acceleration and the effective spring constant of the bridge. Walkers notice discomfort when the maximum acceleration exceeds 0.7 m s⁻². Evaluate whether walkers would be uncomfortable.
[6 marks]
Total for question 4: 12 marks
5
A block of mass 0.30 kg is attached to a horizontal spring of spring constant 48 N m⁻¹ and slides on a smooth air track. It oscillates with simple harmonic motion with an amplitude of 0.045 m.
(a)
What is the total energy of the oscillation?
[1 mark]
A1.1 J
B9.7 × 10⁻² J
C2.4 × 10⁻² J
D4.9 × 10⁻² J
(b)
What is the kinetic energy of the block when its displacement is 0.025 m?
[1 mark]
A1.5 × 10⁻² J
B3.4 × 10⁻² J
C4.9 × 10⁻² J
D6.4 × 10⁻² J
(c)
Calculate the period of the oscillation.
[2 marks]
Total for question 5: 4 marks
6
In a core practical, a student clamps a flexible metal strip at one end and fixes a mass to its free end. A vibrator drives the strip and its frequency is varied to find the resonant frequency. The strip and mass behave like a mass on a spring, and the mass of the strip may be ignored. With a mass of 0.050 kg the resonant frequency is 5.0 Hz.
(a)
The driving frequency is increased slowly from 3 Hz to 7 Hz. Which statement describes the amplitude of the strip?
[1 mark]
AIt increases to a maximum at about 5.0 Hz and then decreases
BIt increases continuously over the whole range
CIt stays constant because the driving force is constant
DIt decreases to a minimum at 5.0 Hz and then increases
(b)
The 0.050 kg mass is replaced by a mass of 0.20 kg. What is the new resonant frequency?
[1 mark]
A10 Hz
B1.3 Hz
C2.5 Hz
D20 Hz
(c)
An unknown mass gives a resonant frequency of 3.5 Hz. Calculate the unknown mass.
[2 marks]
Total for question 6: 4 marks
7
The velocity v of a mass oscillating on a spring is given by v = −0.42 sin(6.0t), where v is in m s⁻¹ and t is in seconds. The displacement is given by x = A cos ωt.
(a)
Determine the amplitude and the period of the oscillation.
[3 marks]
(b)
Calculate the displacement and the acceleration of the mass at t = 0.50 s. Give the direction of the acceleration. Use your calculator in radian mode.
[4 marks]
Total for question 7: 7 marks
8
A student pulls a mass of 0.20 kg on a spring of spring constant 35 N m⁻¹ aside by 6.0 cm and releases it. In air, the amplitude of the oscillation falls to 3.0 cm after 12 complete oscillations. The student then repeats the experiment with the mass immersed in thick oil.
(a)
Describe and explain how the displacement–time graph for the mass in air differs from the graph for the mass in thick oil.
[6 marks]
(b)
Calculate the energy lost by the oscillator in air during the 12 oscillations, as a percentage of its initial energy, and the mean rate at which energy is dissipated.
[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).