IB Questions on Topic 4
Simple Harmonic Motion
1.
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?
3.
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?
4.
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.
Which of the following is the correct expression for the displacement x?
5.
6.
A.
 x 0 cos
B.
x 0 cos
C.
 x 0 sin
D.
x 0 sin
2
t
T
2
t
T
2
t
T
2
t
T
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
A cart, connected to two identical springs, is oscillating with simple harmonic motion between two points
X and Y that are equidistant from point O.
The cart is in equilibrium at
A.
all points between X and Y.
B.
point O only.
7.
C.
points X and Y only.
D.
points O, X and Y only.
This question is about simple harmonic motion and waves.
(a)
A particle of mass m that is attached to a light spring is executing simple harmonic motion in a
horizontal direction.
State the condition relating to the net force acting on the particle that is necessary for it to execute
simple harmonic motion.
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(2)
(b)
The graph shows how the kinetic energy EK of the particle in (a) varies with the displacement x of
the particle from equilibrium.
(i)
Using the axes above, sketch a graph to show how the potential energy of the particle varies
with the displacement x.
(2)
(ii)
The mass of the particle is 0.30 kg. Use data from the graph to show that the frequency f of
oscillation of the particle is 2.0 Hz.
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(4)
(c)
The particles of a medium M1 through which a transverse wave is travelling, oscillate with the
same frequency and amplitude as that of the particle in (b).
(i)
Describe, with reference to the propagation of energy through the medium, what is meant by
a transverse wave.
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(2)
(ii)
The speed of the wave is 0.80 m s–1. Calculate the wavelength of the wave.
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(1)
(d)
The diagram shows wavefronts of the waves in (c) incident on a boundary XY between medium
M1 and another medium M2.
The angle between the normal, and the direction of travel of the wavefronts is 30°.
(i)
The speed of the wave in M1 is 0.80 m s–1. The speed of the waves in M2 is
1.2 m s–1.
Calculate the angle between the direction of travel of the wavefronts in M2 and the normal.
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(3)
(ii)
On the diagram, sketch the wavefronts in M2.
(1)
(Total 15 marks)
8.
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= 
14
x
l
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.
(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)
9.
This question is about simple harmonic oscillations.
Graph 1 shows the variation with time t of the displacement x of a particle P in the medium.
Graph 1
(a)
For particle P,
(i)
state how graph 1 shows that its oscillations are not damped.
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(1)
(ii)
calculate the magnitude of its maximum acceleration.
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(2)
(iii)
calculate its speed at t = 0.12 s.
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(2)
(iv)
state its direction of motion at t = 0.12 s.
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(1)
(b)
Graph 2 shows the variation with position d of the displacement x of particles in the medium at a
particular instant of time.
Graph 2
Determine for the longitudinal wave, using graph 1 and graph 2,
(i)
the frequency.
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(2)
(ii)
the speed.
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(2)
Graph 2 – reproduced to assist with answering (c)(i).
(c)
The diagram shows the equilibrium positions of six particles in the medium.
(i)
On the diagram above, draw crosses to indicate the positions of these six particles at the
instant of time when the displacement is given by graph 2.
(3)
(ii)
On the diagram above, label with the letter C a particle that is at the centre of a compression.
(1)
(Total 14 marks)