4.1 Simple harmonic motion
1a. [4 marks]
This question is about simple harmonic motion (SHM).
The graph shows the variation with time of the acceleration of an object X undergoing simple
harmonic motion (SHM).
Determine the maximum displacement of X. Give your answer to an appropriate number of significant
figures.
1b. [2 marks]
A second object Y oscillates with the same frequency as X but with a phase difference of
using the graph opposite, how the acceleration of object Y varies with .
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. Sketch,
3. [1 mark]
A liquid in a U-tube is given an initial displacement and allowed to oscillate. The motion of the liquid is
recorded using a motion sensor. Which graph shows the variation with time t of the velocity v of the
liquid?
4. [1 mark]
A body undergoes simple harmonic motion. Which graph correctly shows the variation with
displacement x of the velocity v of the body?
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5. [1 mark]
The diagram shows the variation of velocity v with time t for an object performing simple harmonic
motion.
Which of the following shows how the acceleration a varies with t?
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6. [1 mark]
For a body undergoing simple harmonic motion the velocity and acceleration are
A. always in the same direction.B. always in opposite directions.C. in the same direction for a quarter of
the period.D. in the same direction for half the period.
7. [1 mark]
A pendulum swings back and forth in a circular arc between X and Y.
The pendulum bob is
A. always in equilibrium.B. only in equilibrium at X and Y.C. in equilibrium as it passes through the
central position.D. never in equilibrium.
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8. [1 mark]
The graph shows measurements of the height h of sea level at different times t in the Bay of Fundy.
Which of the following gives the approximate amplitude and period of the tides? Test.
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9. [1 mark]
The diagrams show the variation with time t of the displacement y of a particle of a medium through
which a wave travels. Which diagram correctly shows the period T and amplitude A of the wave?
10a. [2 marks]
This question is in two parts. Part 1 is about simple harmonic motion and the superposition of waves.
Part 2 is about gravitational fields.
Part 1 Simple harmonic motion and the superposition of waves
An object of mass m is placed on a frictionless surface and attached to a light horizontal spring. The
other end of the spring is fixed.
The equilibrium position is at B. The direction B to C is taken to be positive. The object is released from
position A and executes simple harmonic motion between positions A and C.
Define simple harmonic motion.
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10b. [3 marks]
(i) On the axes below, sketch a graph to show how the acceleration of the mass varies with
displacement from the equilibrium position B.
(ii) On your graph, label the points that correspond to the positions A, B and C.
10c. [3 marks]
(i) On the axes below, sketch a graph to show how the velocity of the mass varies withtime from the
moment of release from A until the mass returns to A for the first time.
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(ii) On your graph, label the points that correspond to the positions A, B and C.
10d. [3 marks]
The period of oscillation is 0.20s and the distance from A to B is 0.040m. Determine the maximum
speed of the mass.
11. [1 mark]
The graph shows how the displacement varies with time for an object undergoing simple harmonic
motion.
Which graph shows how the object’s acceleration a varies with time t?
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12. [1 mark]
Which graph correctly shows how the acceleration, of a particle undergoing SHM varies with its
displacement,
from its equilibrium position?
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13. [1 mark]
The graph shows how the velocity of an object undergoing simple harmonic motion varies with time
for one complete period of oscillation.
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Which of the following sketch graphs best shows how the total energy
of the object varies with ?
14. [2 marks]
This question is about simple harmonic motion (SHM).
The graph shows the variation with time of the acceleration of an object X undergoing simple
harmonic motion (SHM).
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Define simple harmonic motion (SHM).
15. [1 mark]
Which of the following graphs shows the variation with displacement
performing simple harmonic motion.
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of the speed of a particle
16. [1 mark]
This question is about simple harmonic motion (SHM).
The graph shows the variation with time of the acceleration of an object X undergoing simple
harmonic motion (SHM).
X has a mass of 0.28 kg. Calculate the maximum force acting on X.
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17. [1 mark]
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
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