14.	The graphs show how the acceleration a of four different particles varies with their displacement x.
Which of the particles is executing simple harmonic motion?

15.	The diagram below is a snapshot of wave fronts of circular waves emitted by a point source S at the surface of water. The source vibrates at a frequency f = 10.0 Hz.
		
	The speed of the wave front is
A.	0.15 cm s–1.
B.	1.5 cm s–1.
C.	15 cm s–1.
D.	30 cm s–1.

16.	Two coherent point sources S1 and S2 emit spherical waves.

	Which of the following best describes the intensity of the waves at P and Q?

	P	Q	
A.	maximum	minimum	
B.	minimum	maximum	
C.	maximum	maximum	
D.	minimum	minimum	

17.	This question is about oscillations and waves.
(a)	A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1.

	The length of wood below the surface is d. The wood is pushed vertically downwards a distance A such that a length of wood is still above the water surface as shown in diagram 2. The wood is then released and oscillates vertically. At the instant shown in diagram 3, the wood is moving downwards and the length of wood beneath the surface is d + x.
 
(i)	On diagram 3, draw an arrow to show the direction of the acceleration of the wood.
(1)
 
(ii)	The acceleration a of the wood (in m s–2) is related to x (in m) by the following equation.
		a = 
	Explain why this equation shows that the wood is executing simple harmonic motion.

(b)	The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below, sketch a graph to show how the velocity v of the wood varies with time over one period of oscillation.

(d)	The oscillations of the wood generate waves in the water of wavelength 0.45 m.
The graph shows how the displacement D, of the water surface at a particular distance from the wood varies with time t.

	Using the graph, calculate the
(i)	speed of the waves.

(ii)	ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s.

19.	This question is about a simple pendulum.
(a)	A pendulum consists of a bob suspended by a light inextensible string from a rigid support. The pendulum bob is moved to one side and then released. The sketch graph shows how the displacement of the pendulum bob undergoing simple harmonic motion varies with time over one time period.

	On the sketch graph above,
(i)	label with the letter A a point at which the acceleration of the pendulum bob is a maximum.
(1)
 
(ii)	label with the letter V a point at which the speed of the pendulum bob is a maximum.
(1)
 
(b)	Explain why the magnitude of the tension in the string at the midpoint of the oscillation is greater than the weight of the pendulum bob.

(c)	The pendulum bob is moved to one side until its centre is 25 mm above its rest position and then released.

(i)	Show that the speed of the pendulum bob at the midpoint of the oscillation is 0.70 m s–1.

(ii)	The mass of the pendulum bob is 0.057 kg. The centre of the pendulum bob is 0.80 m below the support. Calculate the magnitude of the tension in the string when the pendulum bob is vertically below the point of suspension.

(d)	The point of suspension of the pendulum bob is moved from side to side with a small amplitude and at a variable driving frequency f.
		
	For each value of the driving frequency a steady constant amplitude A is reached. The oscillations of the pendulum bob are lightly damped.
 
(i)	On the axes below, sketch a graph to show the variation of A with f.