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WorksheetsPre-U Review: Oscillations
Total questions: 46
Worksheet time: 46mins
Which statement best defines the motion of a particle performing simple harmonic motion?
Its displacement x is always given by the expression x = x₀sinωt
It displacement x is related to its velocity v by the expression v = ωx
Its acceleration is always ω2x₀ and is directed at right angles to its motion
Its acceleration is proportional to, and in the opposite direction to, the displacement
For a body moving in simple harmonic motion, which of the following graphs correctly represents its acceleration a varies with its displacement x?
Which of the following graphs shows the variation with displacement r of the resultant force F acting on a particle moving with simple harmonic motion?
A mass hanging from a spring suspended from the ceiling is given a small vertical displacement from its equilibrium position. Which of the following graphs correctly shows the variation of the tension T in the spring with the displacement x of the mass?
A mass, suspended from the end of a spring, is oscillating with simple harmonic motion. If the angular frequency is 2.0 rad s-1, what is the period of the oscillation?
0.080 s
0.32 s
0.50 s
3.1 s
An object is moving in simple harmonic motion with amplitude a. Which graph best shows the variation of its velocity v with its displacement x for one complete oscillation?
The given graph shows how the acceleration a of a particle is related to its displacement x from a fixed point.
Which graph best shows how the speed v is related to x?
If a body, moving in simple harmonic motion, makes n complete oscillations in one second, what is its angular frequency?
n rad s-1
1/n rad s-1
2 π n rad s-1
2 π / n rad s-1
An object is moving in simple harmonic motion about a point P. The given graph shows how its displacement x from P varies with time t.
Which of the following graphs shows how its acceleration a varies with time t?
A spring hangs vertically from the ceiling and a mass is attached to its free end. When the mass is pulled down and released, it oscillates vertically with simple harmonic motion of period T. The variation with time t of its distance from the ceiling is as shown.
Which statement gives a correct deduction from this graph?
The amplitude of the oscillation is 70 cm
The kinetic energy is a maximum at t = 1/2 T
The restoring force on the mass increases between t = 0 and t = 1/4 T
The speed is a maximum at t = 1/4 T
A shooting game involves using a gun that fires by itself at random times. The plater can only point the gun in a fixed direction while the target moves from side to side with simple harmonic motion, as shown.
At which of the given region should the player aim in order to score the greatest number of hits?
3
either 1 or 5
either 2 or 4
any of 1, 2, 3, 4 or 5
At a place where the acceleration of free fall is g, a pendulum swings with a period of 1 s. What is the value of its period when it is swung at another place where the acceleration of free fall is g' ?
The given diagrams show three bodies, represented by P, Q and R, moving in simple harmonic motions.
If the mass of the body is increased, which system will have a longer period?
P only
Q only
P and Q only
Q and R only
The three oscillating systems, represented by p, q and r in the diagrams, each show simple harmonic motion.
In which of these systems will the period be independent of the mass of the body?
p only
q only
r only
p and r only
The water depth in a harbour varies in a simple harmonic manner between 1.0 m at a low tide and 3.0 m at high tide, as illustrated by the graph. The duration between successive low tides is 12 hours. A certain boat requires a minimum depth of water of 1.5 m to enter the harbour.
If such a boat approaches the harbour at low tide, how long will it have to wait before entering?
0.5 hours
1.0 hours
1.5 hours
2.0 hours
Which list consists of quantities that remain constant when a body moves in undamped simple harmonic motion?
A
B
C
D
The variations with time of the displacements of two oscillations are as shown.
Which of the following is the phase difference between the oscillations?
1/4 π rad
1/2 π rad
3/4 π rad
π rad
When a loudspeaker sounds a note of frequency f, the loudspeaker cone will execute simple harmonic motion of amplitude a. What is the maximum acceleration of the cone?
fa
2πfa
(fa)2
(2πf)2a
The displacement x of an object moving in simple harmonic motion is given by the equation x = 30 sin 50t, where t is the time in seconds.
Which of the following is the frequency of oscillation?
0.020 Hz
0.13 Hz
8.0 Hz
30 Hz
The variations with time of two sinusoidal voltages of the same frequency are as shown. Which list correctly gives the frequency of and the phase relationship between the voltages?
A
B
C
D
A simple pendulum has a period of 1 s on the Earth. The acceleration of free fall on the Moon may be taken to be one-sixth of that on the Earth. What is the period of this pendulum on the Moon?
1 / 6 s
1 / √6 s
1 s
√6 s
A body is moving in simple harmonic motion of amplitude 0.020 m and frequency 2.5 Hz. Which of the following is its maximum speed?
0.008 ms-1
0.050 ms-1
0.125 ms-1
0.314 ms-1
The variation with time of the displacement of an oscillating particle is as shown.
Which of the following correctly describes the length PR on the time axis?
half the period
twice the frequency
half the frequency
twice the period
The table shows the corresponding values of the acceleration a and the displacement x of a particle moving in simple harmonic motion.
What is the period of the motion?
1 / π s
2 / π s
π / 2 s
π s
In a simple harmonic motion, the acceleration a is related to the displacement x by the equation a = -ω2 x.
Which expression gives the frequency of the motion?
ω
1 / ω
2 π ω
ω / 2 π
A simple pendulum is suspended from the ceiling of a lift. When the lift is stationary, the pendulum swings with period T₀. When the lift is descending at constant speed, the period is T₁. When its is descending with uniform downward acceleration, the period is T₂.
What is the relationship between the periods T₀, T₁ and T₂ ?
T₀ = T₁ = T₂
T₀ = T₁ < T₂
T₀ = T₁ > T₂
T₀ < T₁ < T₂
For a body oscillating with simple harmonic motion, the variations with time t of its displacement x, velocity v and acceleration a are as shown.
π / 9 s
2π / 9 s
π / 3 s
2π / 3 s
The given graph shows the variation with time of the displacement of a body performing simple harmonic motion.
At which one of the points, A, B, C, or D are the acceleration and velocity in opposite directions?
A
B
C
D
The given graph shows the variation with time of the displacement of a body performing simple harmonic motion.
At which of the given points is the body travelling and accelerating in the same direction?
A
B
C
D
The variation of the potential energy of a body with its displacement from a point Z is as shown. Which aspect of the graph indicates that the force on the body is directed towards Z?
The graph is approximately linear for large displacements
The graph passes through the origin
The potential energy increases as the body moves further from Z
The value of the potential energy is always positive
The given diagram shows a trolley with smooth wheels attached by two light springs to two fixed points P and Q. The trolley of mass 2 kg has a displacement of 0.05 m when a force of 10 N is applied to it. After the force is removed, the equation of the subsequent motion is a = ω2x, where a is the acceleration and x is the displacement from the equilibrium position.
What is the value of the constant ω2?
0.25 rad2 s-2
1.0 rad2 s-2
4.0 rad2 s-2
100 rad2 s-2
The photograph of a simple pendulum was taken when swinging in front of a horizontal scale. It showed that while the camera shutter was open, the bob moved from the 650 mm mark to the 675 mm mark. The period of the pendulum was 2 s and the extreme positions of the bob were at the 600 mm and 700 mm marks.
How long did the shutter remained open?
1 s
1/2 s
1/3 s
1/6 s
An elastic string of unstretched length l₀ is attached to the ceiling at one end. It extends to a total length l when a particle of mass m is suspended at its free end. When the particle is pulled down a small distance b and released, it oscillates in simple harmonic motion described by the equation a + ω2 x = 0, where a is the acceleration and x is the displacement.
Which expression gives the value of ω2 ?
m g / (l - l₀)
m g a / (l - l₀)
g / (l - l₀)
g b / (l - l₀)
The equation describing the motion of a particle is x = 5 sin (2t), where x is the displacement (in m) and t is the time (in s). The value of g may be taken as 10 ms-2. If a simple pendulum has the same period as the particle, what is the length of the pendulum string?
10.0 m
5.0 m
2.5 m
2.0 m
For a particle moving in simple harmonic motion, what is the phase angle between its velocity and its displacement?
π / 4 rad
π / 2 rad
3π / 4 rad
π rad
An object is moving in simple harmonic motion of period T.
Which graph best shows how its kinetic energy E(k) varies with time t?
The given diagram shows a mass m on a smooth horizontal table attached to two fixed supports by two light springs.
The mass is moving in linear simple harmonic motion of amplitude x₀ and period T.
What is the energy associated with the motion
2 π m x₀2 / T2
2 π m2 x₀2 / T
π2 m x₀2 / T2
2 π2 m x₀2 / T2
A certain simple pendulum swings with a period of 2 s. The bob of such a pendulum is given a small displacement and released at time t = 0.
Which diagram correctly shows how the bob's kinetic energy E(k) and its potential energy E(p) varies with time t?
The given graph shows the variation with displacement x of the potential energy U of a particle of mass 4 kg moving in simple harmonic motion.
Which of the following is the period of oscillation of the mass?
A particle is moving in a straight line with simple harmonic motion. Which graph correctly shows the relation between its kinetic energy K, its potential energy V and its total energy T?
A sinusoidal driving force of frequency f is applied to a pendulum of natural frequency f₀. Which graph best shows the variation with f of the amplitude a of the motion?
Due to air resistance, the amplitude of an oscillating pendulum decays exponentially with time. Which of the following correctly describes how the total energy of the pendulum vary with time?
It decays at a steady rate
It decays exponentially
It remains constant
It oscillates about zero
Given the same initial displacement and then released, the variation with time t of the displacements x of two objects P and Q are as shown in the given graphs.
The two objects are then driven by sinusoidal driving forces of the same constant amplitude and of variable frequency f.
Which of the following graphs correctly shows how the amplitudes A of P and Q varies with f?
In an experiment, a pendulum is forced to oscillate at different frequencies f and the response (variation of the amplitude of oscillation with f) is as shown. The experiment is then repeated in a partial vacuum where the damping is significantly less.
Which of the following graphs correctly shows the new response?
The equilibrium height of a car's body above the ground is H₀. At time t = 0, the body of the car is raised slightly to a greater height and released. The car's tyres may be assumed to remain in contact with the ground throughout and its suspension may be taken to be critically damped.
Which graph shows the variation with time of the height of the car body above the ground?
Free electrons in the ionosphere are subjected to a 200 kHz electromagnetic wave in which the electric field oscillates with an amplitude of 5 x 10-3 V m-1.
What is the amplitude of oscillations of these electrons?
3.2 x 10-15 m
4.0 x 10-9 m
2.5 x 10-8 m
5.6 x 10-4 m
