1.	What is meant by simple harmonic motion?
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(2)
Calculate the length of a simple pendulum with a period of 2.0 s.
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 Length = .........................................................
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	The graph shows the variation of displacement with time for a particle moving with simple harmonic motion.

	What is the amplitude of the oscillation?
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(1)

	Estimate the speed of the particle at the point labelled Z.
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 Speed = .........................................................
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	Draw on the axes below a graph of the variation of velocity u with time for this particle over the same period of time.  Add a scale to the velocity axis.

(2)
(Total 9 marks)

2.	A body oscillates with simple harmonic motion.  On the axes below sketch a graph to show how the acceleration of the body varies with its displacement.

(2)

	How could the graph be used to determine T, the period of oscillation of the body?
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A displacement-time graph from simple harmonic motion is drawn below.

	The movement of tides can be regarded as simple harmonic, with a period of approximately 12 hours.
	On a uniformly sloping beach, the distance along the sand between the high water mark and the low water mark is 50 m.  A family builds a sand castle 10m below the high water mark while the tide is on its way out.  Low tide is at 2.00 p.m.
On the graph
(i)	label points L and H, showing the displacements at low tide and the next high tide,
(ii)	draw a line parallel to the time axis showing the location of the sand castle,
(iii)	add the times of low and high tide.
(3)
	Calculate the time at which the rising tide reaches the sand castle.
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Time ......................................................................
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(Total 10 marks)

3.	Define simple harmonic motion.
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	The curve labelled A shows how the displacement of a body executing simple harmonic motion varies with time.

	Add the following to the graph:
(i)	A curve labelled B showing how the acceleration of the same body varies with time over the same time period.
(ii)	A curve labelled C showing how the velocity of the same body varies with time over the same time period.
(4)
Which pair of curves illustrates the definition of simple harmonic motion?
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Explain your answer.
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(Total 9 marks)

4.	A simple pendulum has a period of 2.0 s and oscillates with an amplitude of 10 cm.  
What is the frequency of the oscillations?
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 Frequency = .........................................................
(1)
	At what point of the swing is the speed of the pendulum bob a maximum?
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	Calculate this maximum speed.
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 Maximum speed = .........................................................
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	At what points of the swing is the acceleration of the pendulum bob a maximum?
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	Calculate this acceleration.
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 Maximum acceleration = .........................................................
(3)
(Total 7 marks)

5.	The diagram below shows a mass of 0.51 kg suspended at the lower end of a spring.  The graph shows how the tension, F, in the spring varies with the extension, Dx, of the spring.

Use the graph to find a value for the spring constant k.
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 k = .........................................................
(2)
	The mass, originally at point O, is set into small vertical oscillations between the points A and B.  Choose A, B or O to complete the following sentences.
The speed of the mass is a maximum when the mass is at ..............
The velocity and acceleration are both in the same direction when the
mass is moving from ...... to...... .
(2)
Calculate the period of oscillation T of the mass.
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Period of oscillation T =  .........................................................
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What energy transformations take place while the mass moves from B to O?
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(2)
(Total 8 marks)