Simple Harmonic Motion (Edexcel A Level Physics)

Exam Questions

1 hour12 questions
1a
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2 marks

A student measured the deflection of a mass attached to the end of a thin strip of metal.
The strip was clamped to a bench at one end as shown.

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The student varied the force on the end of the strip by changing the mass attached.

The deflection was measured each time when the mass was in its equilibrium position.

The student obtained the following graph of deflection against force.

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State why the mass will oscillate with simple harmonic motion when it is displaced slightly from its equilibrium position and released.

1b
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5 marks

The student then investigated the oscillations of the mass on the metal strip. The student fixed different numbers of 10 g masses to the end of the metal strip.

The student noticed that the smaller the mass the higher the frequency of the oscillations. He estimated that the maximum number of oscillations he could count was two per second. He decided that the smallest mass he should use was 50 g.

Determine whether 50 g is the smallest mass he should use.

You may assume that the system acts in the same way as a mass on a spring.

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2
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4 marks

A simple pendulum consisting of a thread and a bob is set up next to a horizontal rod.

The bob is displaced to the left and released. When the bob reaches the equilibrium position the thread strikes the horizontal rod. For half of the cycle, only the lower part of the pendulum moves.

The diagram shows the swing of the pendulum.

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The diagram below shows the dimensions of the pendulum.

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Determine the frequency of the oscillations of the pendulum.

(4)

Frequency = ....................................................................

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3a
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9 marks

A student investigated the behaviour of a spring under tension. The spring was hung vertically with a mass holder attached as shown.

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The student measured the length of the spring as he added masses to the holder. The rule was held as shown to measure the distance between the top and bottom coils of the spring. He determined the extension for each value of total mass on the holder. He did this by subtracting the original length of the spring from each extended length.

i)
Explain whether this method would produce accurate values for the extensions of the spring.

(4)

ii)
Explain how the student could modify his method in order to obtain more accurate values for the extensions of the spring.

(5)

3b
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7 marks
In another experiment, the student displaced the mass vertically each time a mass was added to the spring. He used a stopwatch to determine the period of vertical oscillations of each mass.

The student used his data to plot a graph of T2 against m as shown.

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The student expected the graph to be a straight line through the origin. He thought that there may be a systematic error due to reaction time.

i)
Give an example of another possible systematic error in this experiment.

(1)

ii)
Another student suggests that to reduce the uncertainty in the value for the period, a data logger connected to a light gate could be used to measure time.

Comment on the student’s suggestion.

(3)

iii)
Determine a value for the stiffness of the spring.

(3)

 

Stiffness of spring = .......................................................

3c
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3 marks

When determining the period of oscillation for each mass, the student measured the time for 20 oscillations. He repeated this measurement to obtain a mean time for 20 oscillations.

Explain how the student’s procedure contributed to the accuracy of the measurement.

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4a
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6 marks

The diagram shows two identical pendulums, A and B, side by side with a rubber band placed over both strings.

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Pendulum A is displaced and starts to oscillate. As pendulum A oscillates, pendulum B starts to oscillate with the same time period, its amplitude increasing as the amplitude of pendulum A decreases. At one stage pendulum A is no longer oscillating and pendulum B has its maximum amplitude. Then pendulum A starts to oscillate again with increasing amplitude, as the amplitude of pendulum B decreases.

The apparatus is adjusted so that the pendulums do not have the same length as each other. When the first pendulum is set into oscillation, the second pendulum starts to oscillate, but with very small amplitude; the first pendulum does not stop oscillating.

Explain this behaviour.

4b
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4 marks

The graph shows how the displacement of each pendulum varies with time at one stage in the motion.

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i)
State the phase relationship between the two pendulums.

(1)

ii)
Determine the length of pendulums A and B.

(3)





Length = ..................................

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5a
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2 marks

The International Space Station (ISS) is in a low Earth orbit. Astronauts in ISS have an apparent weight of zero. In order to determine their mass, the astronauts must secure themselves to a platform which is set into oscillation and moves with simple harmonic motion.

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Explain why the astronauts in the ISS have an apparent weight of zero.

5b
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2 marks

State what is meant by simple harmonic motion.

5c
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4 marks

Describe how, using a stopwatch and a ruler, the following quantities could be determined for the oscillating platform:

i)
the frequency of oscillation

(2)

ii)
the maximum speed of the platform.

(2)

5d
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2 marks

The platform continues to move with simple harmonic motion at the same frequency, but its amplitude is doubled.

Explain how the maximum kinetic energy of the platform will change.

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6a
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4 marks

The photograph shows an example of a Foucault pendulum. 

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This is a pendulum that consists of a massive sphere, suspended by a long wire from a high ceiling. Over time the vertical plane through which the pendulum swings appears to rotate because of the rotation of the Earth.

mass of sphere = 28.0 kg 

The pendulum makes 8 complete oscillations in 52.2 s
Show that the length of the wire supporting the sphere is about 10 m.
diameter of sphere = 60.0 cm  

6b
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6 marks

During refurbishment, the pendulum is taken down and the wire is replaced.
Steel wires of the following diameters are available:  

0.71 mm 0.91 mm 1.22 mm 1.63 mm 2.03 mm

i)
Explain which of these wires is the thinnest that could be used to support the sphere safely.

breaking stress of steel = 3.10 x 108 N m-2

(3)

ii)
The wire identified in part (i) is used for the pendulum, the unstretched length of the new wire is 11.2 m.

Calculate the extension of the new wire when the sphere is attached.

Young Modulus for steel = 200 GPa 

(3)

Extension = .....................................................

6c
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3 marks

To show the rotation of the Earth, the pendulum needs to oscillate for several hours.
Explain how using a heavy sphere is better than using a light sphere of the same diameter.  

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7a
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9 marks

A trolley is attached to the ends of two springs as shown. When displaced from its equilibrium position, the trolley moves with simple harmonic motion.

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A student has a stopwatch and metre rule available.

i)
Explain the procedure that the student should follow to make an accurate determination of the time period T of the trolley.

(6)

ii)
Describe how the student should use her value of T to determine the maximum speed of the trolley.

(3)

7b
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1 mark

Another student suggests that a more accurate value for T could be obtained by using a position sensor and data logger.

Comment on this suggestion.

7c
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3 marks

The student displaces the trolley a greater distance from the equilibrium position, so the amplitude of oscillation is doubled. The trolley still moves with simple harmonic motion.

Explain how the maximum kinetic energy of the trolley will change.

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1a
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2 marks

A student carried out an experiment with a pendulum hung from a fixed support. The fixed support was a distance h above floor level as shown.

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As the student was unable to measure the length of the pendulum directly, she measured the distance d from the bob to the floor.

To determine the period T of the pendulum, the student used the following method:

  • release the bob from its highest position and start a stopwatch
  • stop the stopwatch when the bob reaches the same position again.

Criticise the student’s method for measuring the period.

1b
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5 marks

The student used her data to plot a graph of T2 against d as shown below.

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Determine a value for the acceleration due to gravity g.

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