Syllabus Edition

First teaching 2020

Last exams 2024

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Damped Oscillations (CIE A Level Physics)

Exam Questions

24 mins3 questions
1a
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5 marks

A bar magnet of mass 250 g is suspended from the free end of a spring, as illustrated in Fig. 3.1.

q3-paper-4-specimen-2022-cie-ial-physics

Fig. 3.1

The magnet hangs so that one pole is near the centre of a coil of wire.
The coil is connected in series with a resistor and a switch. The switch is open.

The magnet is displaced vertically and then allowed to oscillate.

At time t = 0, the magnet is oscillating freely. At time t = 6.0 s, the switch in the circuit is closed.

The variation with time t of the vertical displacement y of the magnet is shown in Fig. 3.2.

q3-2-paper-4-specimen-2022-cie-ial-physics

Fig. 3.2

For the oscillating magnet, use data from Fig. 3.2 to determine, to two significant figures:

(i)
the frequency f



f = ...................................... Hz [2]

(ii)
the energy of the oscillations during the time interval t = 0 to t = 6.0 s.





energy = ....................................... J [3]

1b
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1 mark

When the switch is closed, the oscillations are damped.

Explain, with reference to Fig. 3.2, whether this damping is light, critical or heavy.

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2a
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2 marks

Fig. 1.1 shows a light pendulum and a heavy pendulum, both suspended from the same piece of copper wire. This copper wire is secured at each end to fixed points.

17-2-2a-m-oscillating-pendulums-sq-cie-a-level

Both pendulums have the same natural frequency. 

The heavy pendulum is set to oscillate perpendicular to the plane of the diagram. As it oscillates, it causes the light pendulum to oscillate.  

State what is meant by resonance.

 

2b
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3 marks

Fig. 1.2 shows the variation with time of the displacements of the two pendulums for three oscillations. 

17-2-2b-m-oscillating-pendulums-graph-sq-cie-a-level 
The variation with of the displacement of the light pendulum is given by
 
x space equals space 0.5 space sin space open parentheses 2.5 pi space t close parentheses
 
where is in metres and is in seconds.
 
Calculate the frequency, of the oscillations.
 
f = ........................................... Hz 

2c
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2 marks

On Fig. 1.2, label both axes with the correct scales. Use the space below for any additional working that you need. 

 
2d
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3 marks
(i)
Define phase difference, Φ.
[1]
 
(ii)
Determine the magnitude of the phase difference Φ between the oscillations of the light and heavy pendulums. Give a unit with your answer.
 
Φ = ................................................ unit ............ [2]

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3a
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4 marks

For an oscillating body, state what is meant by: 

(i)
 forced frequency,
[1] 
(ii)
natural frequency of vibration,
[1] 
(iii)
resonance.
[2]
3b
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2 marks

State and explain one situation where resonance is useful.

 
3c
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2 marks

In some situations, resonance should be avoided.
State one such situation and suggest how the effects of resonance are reduced.

 

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