WorksheetsSimple Harmonic Motion Quiz
Total questions: 98
Worksheet time: 2hrs 19mins
What is Simple Harmonic Motion (SHM)?
A circular motion around a fixed point
A random motion with no pattern
A linear motion without any oscillation
A repetitivve motion about an equilibrium position.
What is the frequency of oscillation in Simple Harmonic Motion?
The time it takes for the object to complete one full cycle of motion.
The rate of change of angular displacement.
The number of cycles completed in a unit of time.
The maximum displacement from the equilibrium position.
An object undergoes simple harmonic motion with a period of 0.40 s. The distance between the extreme positions of the object is 6.0 cm. What is the frequency and amplitude of the motion?
0.40 Hz 3.0 cm
2.5 Hz 3.0 cm
0.40 m 6.0 cm
2.5 m 6.0 cm
A child on a swing performs 0.2 oscillations per second. What is the period of the oscillation?
0.2 Hz
5.0 Hz
6.3 Hz
31 Hz
The pendulum of a wall clock completes 25 oscillations in 30 s. What is the period and frequency of oscillation?
0.83 s 1.2 Hz
1.2 s 0.83 Hz
30 s 0.03 Hz
0.03 s 750 Hz
A spring emerges from a fully compressed position to a fully extended position in 1.5 seconds. Calculate the angular frequency of the cuckoo as it emerges from the clock.
0.67 rad/s
1.5 rad/s
2.1 rad/s
4.2 rad/s
A force F acting on a point mass depends on the displacement ! of the mass. Which of the relationships between F and ! leads to simple harmonic motion?
F = -k!
F = -2k!
F = 3k!
F = 4k!
What is the restoring force in Simple Harmonic Motion?
A force that pulls the object back towards the equilibrium position.
A force that changes the direction of motion.
A force that pushes the object away from the equilibrium position.
A force that keeps the object stationary.
What does the negative sign in the equation for simple harmonic motion indicate?
The acceleration is constant regardless of displacement.
The direction of the acceleration is opposite to the displacement.
The direction of the acceleration is the same as the displacement.
The acceleration is not related to displacement.
The defining equation of SHM describes the relationship between acceleration, (angular frequency, ), and displacement, !, from the equilibrium position: a = -ω²x. Which value correctly shows the resulting acceleration if the angular frequency was doubled?
-4ω²
1/4ω²
2ω²
4ω²
Which graph correctly represents the relationship between acceleration (a) and displacement (x) in simple harmonic motion?
Graph A
Graph B
Graph C
Graph D
A acceleration (a) of a body executing simple harmonic motion varies with its displacement (x) from a fixed point as shown below. What is the angular frequency, ω, of the body?
4.5 rad/s
6.3 rad/s
20 rad/s
400 rad/s
When does the acceleration reach its maximum value in Simple Harmonic Motion?
At the minimum displacement
At the maximum displacement
At half the amplitude
At the equilibrium position
For a spring-mass system, the spring constant is 5.0 N/m and the mass is 0.20 kg. Find the magnitude of acceleration when the mass is displaced through a distance of 0.15 m.
3.75 m/s²
4.33 m/s²
5.77 m/s²
6.67 m/s²
Which of the following correctly represents the angular frequency of an oscillating spring-mass system?
ω = k/m
ω = -k/x
ω = √(k/m)
ω = k/x
A student carries out the experiment and checks that it seems to be working by using one set of measurements to determine the spring constant: Mass: 0.20 kg, Period: 1.20 s. What is the spring constant for the spring from this data?
5.48 N/m
52.3 N/m
137 N/m
164 N/m
A simple pendulum and a mass-spring system oscillate about their equilibrium positions with simple harmonic motion. On Earth, the period of the oscillations is T. The pendulum and the mass-spring system are taken to Mars where the acceleration of free fall is smaller than on earth. Which answer best describes the period of the pendulum and the mass-spring system on Mars?
T. Greater than T.
T. T.
Greater than T. Greater than T.
Greater than T. T.
A simple pendulum oscillates with simple harmonic motion as shown. At which positions are the acceleration at zero, the displacement at a negative maximum, and velocity at a maximum?
Z Y X
Y X Y
X Z Z
Y X Z
What provides the restoring force for a simple pendulum?
Friction
Tension in the string
Gravity
Air resistance
Which of the following expressions represent the restoring force for an oscillating pendulum?
F = -mg cos(θ)
F = -mg sin(θ)
F = -mg tan(θ)
F = -mg
What is the period of a simple pendulum whose length is 0.80 m?
0.045 s
0.51 s
1.8 s
22 s
A simpler way of finding T is to use a swinging pendulum. Which of the following equations show the relationship between the length L of the pendulum, its period T, and gravitational field strength g?
T = 2π√(L/g)
T = 2π√(L/g)
T = 2π√(L/g)
T = 2π√(L/g)
Identify the correct equation for the total energy of a system in simple harmonic motion.
=>$−>#
=>$×>#
=>#/√$
=>$+>#
At which position is the kinetic energy of the block a maximum?
A only
B only
C only
A and C
The total energy of an undamped system oscillating in SHM is ______.
Variable
Zero
Maximum
Constant
Which graph correctly shows how kinetic energy of an oscillator varies as a function of time through one complete oscillation?
A
B
C
D
Explain why a person jumping on a trampoline is not an example of simple harmonic motion.
A pendulum is swinging with a frequency of 0.5 Hz. What is the size and direction of the acceleration when the pendulum has a displacement of 2.0 cm to the right?
The graph of acceleration against displacement for an object performing SHM is shown. Complete the statements below: The ________ negative _______ gradient of the graph represents the ________ minus _________ sign in the equation. This sign shows that displacement is measured ________ out from ________ the equilibrium position, but the acceleration is always ________ towards _______ this point. They are in opposite directions.
Calculate the time period and frequency of a mass of 2.0 kg attached to a spring with a spring constant of 0.9 N/m oscillating with simple harmonic motion.
An object of mass 0.45 kg is attached to a spring with spring constant 12 N/m. The object undergoes simple harmonic motion with an amplitude of 0.15 m. Calculate the period of oscillation.
A mass-spring system undergoes simple harmonic oscillations of a frequency 0.58 Hz. Calculate the spring constant.
Which two statements correctly complete the sentence below about simple harmonic motion? 'An object undergoes simple harmonic motion (SHM) when its acceleration is always...'
A simple pendulum executes simple harmonic motion. Identify the forces acting on the pendulum below when it is displaced through a small angle.
A pendulum has a period of 1.23 s. Determine the length of this pendulum if it is located near the surface of the earth.
Which of the factors is NOT a factor affecting the period of a simple pendulum?
A system executing simple harmonic motion has a potential energy of 0.80 J when the displacement is at a maximum. At equilibrium, the kinetic energy of this system is (a) .
When the potential energy is 0.80 J, the speed of this system is (a) .
Complete the table to describe the potential and kinetic energies at X, Y and Z in the motion of a simple pendulum. Use the terms zero or maximum.
The figure below shows the energy graphs for an object in SHM. Identify which of the labeled graphs A, B and C represents total energy, kinetic energy, and potential energy.
What is the amplitude of the oscillator?
Which two of the following statements concerning the total energy in SHM are correct?
Which of the following conditions must be fulfilled for two travelling waves to become a standing wave?
Which of the following conditions must be fulfilled for two travelling waves to become a standing or stationary wave?
The two waves must have the same frequency.
The two waves must have the same amplitude.
The two waves must superpose.
The two waves must be travelling in opposite directions.
Which process causes the standing waves to form on the string?
A pair of waves with different frequencies and similar amplitudes.
Superposition of two waves of the same frequency and amplitude travelling in the same direction.
A single wave with a speed of zero.
Superposition of two waves of the same frequency and amplitude travelling in the opposite direction.
Which of the following is a correct statement about a standing wave?
A standing wave transfers energy.
The two waves must be travelling at different speeds but have the same frequencies.
It is formed when two waves travelling in the same direction superpose.
It contains nodes and antinodes.
What distinguishes progressive waves from standing waves?
Progressive waves transfer energy, while standing waves do not.
Progressive waves remain localized, while standing waves propagate.
Progressive waves have nodes and antinodes.
Progressive waves are always sinusoidal.
Which of the following shows the correct reflection of the wave for this case?
Which of the following relates the node and antinode correctly to the labeled points A and B on the figure?
Node A Antinode B
Node B Antinode A
Node A Antinode A
Node B Antinode B
What is the distance between adjacent nodes (or antinodes) in a standing wave?
One wavelength
Half a wavelength
Two wavelengths
Quarter wavelength
What are the points on a standing wave where there is minimal displacement called?
Antinodes
Nodes
Troughs
Crests
What is the amplitude at the antinodes in a standing wave?
Zero
Minimum
Maximum
Variable
What is the phase difference between particles in adjacent nodal regions of a standing wave?
0 degrees
90 degrees
180 degrees
270 degrees
What type of oscillation occurs when there are only internal forces acting and no energy input?
Standing waves
Resonant oscillations
Free oscillation
Forced oscillations
What is the term for oscillations produced by a periodic external force?
Standing waves
Resonant oscillations
Free oscillation
Forced oscillations
When the frequency of the applied force to an oscillating system is equal to its natural frequency, what phenomenon occurs?
Reflection
Resonance
Diffractioin
Refraction
What is the lowest frequency mode of a standing wave formed on a string called?
First harmonic or fundamental mode
Second harmonic
Third harmonic
Resonant frequency
In an experiment to demonstrate a standing wave in a string, the string is fixed at both ends and attached to a vibration generator. As the frequency is increased until it matches the natural frequency of a particular length of string, a standing wave with one 'loop' will be seen. Which of the following statements are correct?
The fixed ends are nodes.
The fixed ends are antinodes.
The centre is an antinode.
This is the first harmonic.
When a string vibrates in its fundamental mode, what is its wavelength in terms of the length of the string?
Q=O/2
Q=O/4
Q=2O
Q=4O
What is the speed of the wave traveling through a string if the frequency of the 3rd harmonic on a 2 m long string is 300 Hz?
100 m/s
200 m/s
400 m/s
600 m/s
If a string is 3 meters long and the 4th harmonic is produced, what is the wavelength of the harmonic?
0.25 m
0.50 m
0.75 m
1.50 m
The frequency of the standing wave below is 100 Hz. What is its fundamental frequency?
25 Hz
50 Hz
100 Hz
200 Hz
If the fundamental frequency for a stringed instrument is 500 Hz, which of the following are the correct values of its first 3 harmonics?
750 Hz, 1000 Hz, 1250 Hz
1000 Hz, 1500 Hz, 2000 Hz
1000 Hz, 2000 Hz, 3000 Hz
1500 Hz, 2500 Hz, 3500 Hz
In organ pipes (one end closed), where do nodes typically form?
At the closed end
At the open end
At the center
At random points
What are the number of nodes and antinodes formed?
2 antinodes and 2 nodes
2 antinodes and 3 nodes
3 antinodes and 2 nodes
3 antinodes and 3 nodes
Which of the following represent the correct expression for the wavelength of the wave?
4O
4O/2
4O/3
4R O
Which of the following represent the correct expression for the frequency of the wave?
R/4O
R/2O
R/O
4R O
Strings and the air in pipes can be set into oscillation and produce standing waves. The shape of the standing waves determines the harmonic. Which of the following
Which of the following statements about harmonics is not correct?
Pipes which are closed at one end only produce odd numbered harmonics.
Pipes which are open at both ends can produce odd and even numbered harmonics.
Strings which are fixed at both ends can produce odd and even numbered harmonics.
Pipes which are open at both ends can produce only odd numbered harmonics.
Which of these does not provide a damping force to a moving car?
Air resistance
Turbulence
Power steering
Friction
Which of the following are examples of resonance being potentially useful?
1 and 3 only
2 and 4 only
2, 3 and 4 only
All of the above
State if the following statements are true or false?
In the table below, differentiate between progressive (traveling) waves and standing waves.
Describe the behavior of waves under the following boundary conditions: Fixed End and Free End.
Complete the statements below.
Complete the table by stating and explaining whether the given scenarios are examples of free or forced oscillations.
Complete the statements by filling in the blanks.
Complete the table below by identifying the harmonic for each of the given figures.
A guitar string of length 66 cm vibrates in its first harmonic mode of frequency 380 Hz. Calculate the speed of the waves on the string.
A standing wave is set up on a string of length 60 cm fixed at both ends, as shown. The speed of the wave on the string is 380 m/s. Calculate the frequency of the standing wave.
State the phase difference between the oscillations of the two points.
A fourth harmonic standing wave of wavelength 0.16, is formed on a string that is fixed at both ends. On the figure above, draw the standing wave formed.
Complete the table below regarding the standing wave.
Calculate the length of the string.
Calculate the speed of sound in the pipe.
Calculate the first two harmonic frequencies that can be produced in a tube of length 0.50 m that is open at both ends.
Calculate the first harmonic frequency for a tube open at one end and closed at the other.
On the diagrams draw lines to represent the waveforms of the fundamental (first harmonic) resonant note for each pipe.
What is the Doppler effect?
A change in the speed of light waves.
A change in the volume of waves.
A change in the amplitude of sound waves.
A change in the frequency of waves perceived by an observer due to relative motion.
The source is moving towards _______.
Point A
Point B
Point C
Point D
Compared with the frequency of the waves observed at C, the frequency of the waves observed at A is _______.
lesser
greater
the same
zero
What happens to the pitch of a passing ambulance siren as it moves towards you?
Increases
Decreases
Remains the same
Stops
A train moving with a speed of 30 m/s sounds a 150 Hz horn. What frequency is heard by an observer standing near the tracks as the train approaches the observer? Use 343 m/s for the speed of sound.
138 Hz
142 Hz
156 Hz
164 Hz
In the Doppler effect, what happens to light waves when a source is moving away from an observer?
Blue shift - increase in frequency towards the blue end of the spectrum
Blue shift - decrease in frequency towards the blue end of the spectrum
Red shift - decrease in frequency towards the red end of the spectrum
Red shift - increase in frequency towards the red end of the spectrum
What does a red shift in the light from a star indicate?
The star is stationary
The star is moving towards Earth
The star is moving away from Earth
The star is changing color
An ultraviolet wavelength of 85.0 nm is observed in the spectrum of a distant galaxy. A corresponding stationary source on Earth emits a wavelength of 78.0 nm. Which of the following is correct regarding the direction of motion of the galaxy relative to the Earth and the shift of light.
Towards the Earth Red shift
Towards the Earth Blue shift
Away from the Earth Red shift
Away from the Earth Blue shift
A stationary siren emits sound of frequency 800 Hz. The speed of sound is 340 m/s. A cyclist is moving towards the siren with a constant speed of 9.0 m/s. calculate the frequency heard by the cyclist.
Passengers of a car moving away from the siren hear a frequency of 750 Hz. Calculate the speed of the car.
