CIE A Level Physics

Topic Questions

A LevelPhysicsCIETopic Questions17. Oscillations17.1 Simple Harmonic Motion

Syllabus Edition

First teaching 2020

Last exams 2024

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17.1 Simple Harmonic Motion

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1a
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Define an oscillation.

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1b
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Identify the correct definition by drawing lines between the properties of oscillations and their definition.

 
Properties of Oscillations   Definition of Properties
Displacement  

 

The rate of change of angular displacement with respect to time
Amplitude  

  

The distance of an oscillator from its equilibrium position
Angular Frequency  

 

The time taken for one complete oscillation
Frequency  

 

The maximum displacement of an oscillator from its equilibrium position
Time Period  

 

The number of oscillations per unit time

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1c
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Define simple harmonic oscillation.

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1d
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Use the words in the box below to correctly label the diagram of an oscillating pendulum in Fig 1.1.

 
displacement of mass          mass          acceleration          restoring force          equilibrium position

 

17-1-1d-e-shm-diag-label-esq-cie-a-level
Fig. 1.1

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2a
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Identify by drawing a circle around the equation that defines simple harmonic motion and its two solutions.

 
v space equals space f lambda omega space equals space fraction numerator 2 pi over denominator T end fraction x space equals space x subscript 0 sin open parentheses omega t close parentheses
x equals x subscript 0 cos open parentheses omega t close parentheses a space equals space minus space omega squared x f space equals space 1 over T

 

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2b
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The graph in Fig. 1.1 shows that the acceleration of an object is directly proportional to the negative displacement.

 
17-1-2b-e-shm-eqn-graph-to-label-esq-cie-a-level
Fig. 1.1
 
Label the two axis of the graph on Fig. 1.1.

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2c
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The graphs in Fig. 1.3 show an oscillator starting at the equilibrium position and an oscillator starting at the maximum displacement.

17-1-2c-e-shm-graphs-diff-starting-positions-esq-cie-a-level
Fig. 1.3
 
Identify by writing next to the graphs on Fig 1.3 the correct name of the starting position of the oscillator. 
 

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2d
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The equation below defines how the speed of an oscillator changes with the displacement of the oscillator.

       v space equals space plus-or-minus omega square root of open parentheses x subscript 0 space minus space x close parentheses end root 

Identify the variables in the equation by stating the variable and the quantity it represents in the space below. 

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3a
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Complete the gaps, using the words from the box, in the sentences that describe the relationship between the simple harmonic motion graphs.

 
cosine     sine     identical     motion     displacement     45°     90°     velocity

 

  • The displacement-time graph is a curve identical to a _____________ graph when the oscillator starts from its equilibrium position.

 

  • Velocity is the rate of change of _____________

 

  • The velocity-time graph is _____________ out of phase with the displacement-time graph

 

  • Acceleration is the rate of change of _____________

 

  • The acceleration-time graph is _____________ to the displacement graph except reflected on the x-axis.

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3b
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State the equation for the total energy of a simple harmonic system.

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3c
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Fig. 1.1 shows the graph of potential, kinetic and total energy of a simple harmonic system for half a period of simple harmonic oscillation. 

 17-1-3c-e-energy-graph-esq-cie-a-level
Fig. 1.1
 
Match the labels to the correct place on the graph by drawing a line between them.

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3d
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Identify, by placing a tick (✓) next to, the correct statements about the key features of the displacement-time graph. 

 
Possible statements about the displacement-time graphs Place a tick (✓) here if the statement is correct

 

The amplitude of oscillations x0 can be found from the maximum value of x

  

 

If the oscillations start at the positive or negative amplitude, the displacement will be at its minimum

  

 

The time period of oscillations T can be found from reading the time taken for one full cycle

  

 

The graph always starts at 0

  

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1a
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A pendulum consists of a bob (small plastic sphere) attached to the end of a piece of wire. The other end of the wire is attached to a fixed point. The bob oscillates with small oscillations about its equilibrium position, as shown in Fig. 1.1.

17-1-2a-m-pendulum-bob-sq-cie-a-level

The length L of the pendulum, measured from the fixed point to the centre of the bob, is 1.56 m.

 

The acceleration a of the bob varies with its displacement x from the equilibrium position as shown in Fig. 1.2.

17-1-2a-m-pendulum-bob-sq-graph-cie-a-level

State how Fig. 1.2 shows that the motion of the pendulum is simple harmonic. 

 

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1b
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Use Fig. 1.2 from (a) to calculate the angular frequency ω of the oscillations.

 
ω = ................................................. rad s−1 

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1c
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The angular frequency ω is related to the length L of the pendulum by 

 omega space equals space square root of k over L end root 

where k is a constant. 

Use your answer from (b) to determine k. Give a unit for your answer.

 
k = ............................................... unit ................ 

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1d
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Whilst the pendulum is oscillating, the length of the string is decreased in such a way that the total energy of the oscillations remains constant. 

Suggest and explain the qualitative effect of this change on the amplitude of the oscillations.

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2a
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An object is suspended from a spring that is attached to a fixed point as shown in Fig. 1.1.

17-1-3a-m-object-on-spring-sq-shm-cie-a-level

The object oscillates vertically with simple harmonic motion about its vertical position. 

 

State the defining equation for simple harmonic motion. Identify the meaning of each of the symbols used to represent Physical quantities. 

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2b
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The variation with displacement x from the equilibrium position of the velocity v of the object is shown in Fig. 1.2.

17-1-3b-m-displ-vel-graph-sq-shm-cie-a-level
 
Use Fig. 1.2 to:
 
(i)
Determine the amplitude x0 of the oscillations
 
x0 = .............................................. m [1]
 
(ii)
Determine the angular frequency ω of the oscillations.
[2]

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2c
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The oscillations of the object are now heavily damped.

(i)
State what is meant by damping.                              [2]
 
(ii)
Assume that the damping does not change the angular frequency of the oscillations.
 
On Fig. 1.2, sketch the variation with x of v when the amplitude of the oscillations is 0.03 m.
[2]

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