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SHM Name

1. The graph below shows the variation with time t of the displacement x of a particle undergoing simple harmonic motion.

[pic]

Which graph correctly shows the variation with time t of the acceleration a of the particle?

[pic]

(Total 1 mark)

2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

[pic]

Which graph shows how the object’s acceleration a varies with time t?

[pic]

(Total 1 mark)

3. For a system executing simple harmonic motion, the restoring force acting on the system is proportional to the

A. displacement of the system from equilibrium.

B. amplitude of oscillation.

C. elastic potential energy.

D. frequency of oscillation.

(Total 1 mark)

4. Which of the following graphs shows the variation with displacement x of the speed v of a particle performing simple harmonic motion.

[pic]

(Total 1 mark)

5. A particle performs simple harmonic oscillations. Which of the following quantities will be unaffected by a reduction in the amplitude of oscillations?

A. The total energy

B. The maximum speed

C. The maximum acceleration

D. The period

(Total 1 mark)

6. A particle oscillates with simple harmonic motion with period T.

At time t = 0, the particle has its maximum displacement. Which graph shows the variation with time t of the kinetic energy Ek of the particle?

[pic]

(Total 1 mark)

7. 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?

[pic]

(Total 1 mark)

8. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the variation with time t of the displacement x. The amplitude is x0 and the period of oscillation is T.

[pic]

Which of the following is the correct expression for the maximum acceleration of the object?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

(Total 1 mark)

9. Which of the following is the correct expression for the displacement x?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

(Total 1 mark)

10. 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.

[pic]

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.

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(3)

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

[pic]

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

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(2)

(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.

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(3)

11. 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.

[pic]

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.

(ii) The acceleration a of the wood (in m s–2) is related to x (in m) by the following equation.

a = [pic]

Explain why this equation shows that the wood is executing simple harmonic motion.

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(2)

(iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is 0.70 m.

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(3)

(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.

[pic]

(1)

(c) The distance A that the wood is initially pushed down is 0.12 m.

(i) Calculate the magnitude of the maximum acceleration of the wood.

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(2)

(ii) On your sketch graph in (b) label with the letter P one point where the magnitude of the acceleration is a maximum.

(1)

(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.

[pic]

Using the graph, calculate the

(i) speed of the waves.

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(2)

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

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(2)

(iii) ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s

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(1)

(Total 15 marks)

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