Simple Harmonic Motion (Edexcel A Level Physics)

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.

The diagram below shows the dimensions of the pendulum.

Determine the frequency of the oscillations of the pendulum.

(4)

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

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

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.

(4)

(5)

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.

(1)

Comment on the student’s suggestion.

(3)

(3)

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

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.

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

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.

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

(1)

(3)

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

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.

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

State what is meant by simple harmonic motion.

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

(2)

(2)

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.

The photograph shows an example of a Foucault pendulum. 

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  

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

(3)

(3)

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

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.  

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.

A student has a stopwatch and metre rule available.

(6)

(3)

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.

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.