Define simple harmonic motion (SHM) .

A repetitive oscillation about an equilibrium position , in which the restoring force (and therefore the acceleration ) is directly proportional to the displacement from equilibrium and always directed towards it.

List four examples of oscillators that undergo simple harmonic motion.

The pendulum of a clock A child on a swing A mass on a spring Guitar strings vibrating The vibrations of a bowl A bungee jumper reaching the bottom of his fall

Why does a person bouncing on a trampoline not undergo simple harmonic motion?

The restoring force is not proportional to the displacement . While the person is not in contact with the trampoline, the restoring force is equal to their weight , which is constant and always acts downwards.

If an oscillator starts at its position of maximum displacement ( t = 0), the displacement equation is x = A .......... (⍵ t ).

If an oscillator starts at its position of maximum displacement ( t = 0), the displacement equation is x = A cos (⍵ t ).

True or False? The time period of an oscillator undergoing SHM increases as its amplitude of oscillation increases.

False. For small angles of oscillation, the time period of SHM is independent of the amplitude of oscillation.

Define periodic function , in the context of undamped SHM graphs.

A function that repeats itself at regular intervals . All undamped SHM graphs are periodic functions, so can be described by sine and cosine curves.

How is the velocity of an oscillator at any instant found from its displacement-time graph?

It is equal to the gradient of the displacement-time graph at that instant.

At what point in an oscillation is an oscillator's velocity at a maximum ?

At the equilibrium position , where displacement x = 0.

The acceleration-time graph is a .......... of the displacement-time graph in the x -axis.

The acceleration-time graph is a reflection of the displacement-time graph in the x -axis.

At what displacement is an oscillator's acceleration at a maximum ?

At its maximum displacement (the amplitude position).

True or False? The velocity-time graph and acceleration-time graph of an oscillator in SHM are in phase with each other.

False. The displacement, velocity and acceleration graphs of an oscillator in SHM are all 90° out of phase with each other.

At what point in an oscillation does an oscillator have its maximum acceleration ?

At its maximum displacement (the amplitude position, x = A ).

The acceleration of an oscillator is .......... at the equilibrium position.

The acceleration of an oscillator is zero at the equilibrium position.

True or False? An oscillator has its maximum speed at its position of maximum displacement.

False. Maximum speed occurs at the equilibrium position ; at maximum displacement (the amplitude) the speed is zero .

Does the time period of a mass-spring system depend on the gravitational field strength?

No. The equation does not include g , so the oscillations would have the same time period on Earth and the Moon.

The equation for the time period of a mass-spring system applies to both .......... and .......... mass-spring systems.

The equation for the time period of a mass-spring system applies to both horizontal and vertical mass-spring systems.

True or False? A spring with a higher spring constant has a longer time period of oscillation.

False. A higher spring constant makes a stiffer spring, which gives a shorter time period of oscillation.

Define a simple pendulum .

A string and bob , where the bob is a weight (generally spherical, treated as a point mass) that moves side to side. The string is light and inextensible , remains in tension throughout, and is attached to a fixed point above the equilibrium position.

Does the time period of a simple pendulum depend on the gravitational field strength?

Yes. Its time period would be different on the Earth and the Moon.

The time period equation for a simple pendulum is only valid for .......... angles of oscillation, where θ < 10°.

The time period equation for a simple pendulum is only valid for small angles of oscillation, where θ < 10°.

True or False? For the small angle approximation, the restoring force on a pendulum bob is assumed to act vertically.

False. It is assumed the restoring force acts horizontally , towards the equilibrium position (since sin θ ≅ θ for small angles).

Give an example of a harmonic oscillator, other than a pendulum or mass-spring system.

Liquid oscillating in a U-tube .

The time period equation for liquid oscillating in a U-tube is the same as the equation used for a .......... .

The time period equation for liquid oscillating in a U-tube is the same as the equation used for a simple pendulum .

True or False? The time period equation for a U-tube oscillator uses the total length of the U-tube.

False. It uses l , the length of the liquid column only, not the total length of the tube.

Why does water oscillating in a U-tube undergo simple harmonic motion?

Its restoring force is proportional to its displacement from the equilibrium position, as with a spring or pendulum.

In a horizontal mass-spring system oscillating in SHM, at which position is the elastic potential energy maximum, and at which is it minimum?

Maximum at the amplitude position, where the spring is fully stretched Minimum (zero) at the equilibrium position

In a simple pendulum oscillating in SHM, at which position is the gravitational potential energy maximum, and at which is the kinetic energy maximum?

Gravitational potential energy is maximum at the amplitude position (top of the swing) Kinetic energy is maximum at the equilibrium position

On the energy-displacement graph for SHM, potential energy is represented by a .......... shaped curve, while kinetic energy is represented by a .......... shaped curve.

On the energy-displacement graph for SHM, potential energy is represented by a 'U' shaped curve, while kinetic energy is represented by a 'n' shaped curve.

Why does the energy-time graph for a simple pendulum in SHM never show negative values on the y-axis?

Energy is always positive , so an SHM energy-time graph drawn with negative energy values is incorrect.

True or False? On an energy-displacement graph for SHM, the total energy is represented by a curve that peaks at the amplitude position, in the same way as the potential energy curve.

False. The total energy is represented by a horizontal straight line above the potential and kinetic energy curves, since it remains constant throughout the oscillation.

What is the resolution of a stopwatch and a metre ruler typically used in this required practical?

Stopwatch: ±0.01 s Metre ruler: ±1 mm

In the mass-spring SHM experiment used to determine the spring constant , state the independent, dependent and control variables.

Independent variable: mass , m Dependent variable: time period , T Control variables: spring constant, k and number of oscillations

In the simple pendulum experiment used to determine acceleration due to gravity , state the independent, dependent and control variables.

Independent variable: length , L Dependent variable: time period , T Control variables: mass of pendulum bob and number of oscillations

Why is the time for ten complete oscillations measured and then divided by ten, rather than timing a single oscillation?

To reduce the random error in the measured time period, for example the error introduced by reaction time when starting and stopping the stopwatch.

One complete oscillation of a pendulum is counted from the equilibrium position, to one .......... , to the other maximum, and back to equilibrium again.

One complete oscillation of a pendulum is counted from the equilibrium position, to one maximum , to the other maximum, and back to equilibrium again.

State one systematic error and one random error precaution used in this required practical.

Systematic: reduce parallax error by viewing the marker at eye level Random: keep oscillation amplitudes small, use the same starting angle or displacement each time, and repeat any pendulum readings that do not swing in a straight line

True or False? In the pendulum required practical, one complete oscillation is counted as the pendulum swinging from one side to the other side.

False. One complete oscillation is counted from the equilibrium position , to one maximum, to the other maximum, and back to the equilibrium position again, not just from side to side.

A LevelPhysicsAQAFlashcardsFurther Mechanics & Thermal PhysicsSimple Harmonic Motion

Simple Harmonic Motion (AQA A Level Physics): Flashcards

Exam code: 7408

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FrontConditions for Simple Harmonic Motion
Define simple harmonic motion (SHM).
FrontConditions for Simple Harmonic Motion
State the defining equation of SHM and give the meaning of each symbol.
BackConditions for Simple Harmonic Motion
$a = - ω^{2} x$
a = acceleration (m s^-2)
⍵ = angular frequency (rad s^-1)
x = displacement (m)
The minus sign shows a and x are always in opposite directions
FrontConditions for Simple Harmonic Motion
List four examples of oscillators that undergo simple harmonic motion.
BackConditions for Simple Harmonic Motion
The pendulum of a clock
A child on a swing
A mass on a spring
Guitar strings vibrating
The vibrations of a bowl
A bungee jumper reaching the bottom of his fall

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Cards in this collection (55)

Define simple harmonic motion (SHM).
A repetitive oscillation about an equilibrium position, in which the restoring force (and therefore the acceleration) is directly proportional to the displacement from equilibrium and always directed towards it.
State the defining equation of SHM and give the meaning of each symbol.
$a = - ω^{2} x$
- a = acceleration (m s^-2)
- ⍵ = angular frequency (rad s^-1)
- x = displacement (m)
The minus sign shows a and x are always in opposite directions
List four examples of oscillators that undergo simple harmonic motion.
- The pendulum of a clock
- A child on a swing
- A mass on a spring
- Guitar strings vibrating
- The vibrations of a bowl
- A bungee jumper reaching the bottom of his fall
Why does a person bouncing on a trampoline not undergo simple harmonic motion?
The restoring force is not proportional to the displacement. While the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant and always acts downwards.
If an oscillator starts at its position of maximum displacement (t = 0), the displacement equation is x = A .......... (⍵t).
If an oscillator starts at its position of maximum displacement (t = 0), the displacement equation is x = A cos (⍵t).
Give the equation for the speed of an oscillator in SHM at displacement x, defining A.
$v = \pm ω \sqrt{A^{2} - x^{2}}$
A = amplitude (m)
True or False?
The time period of an oscillator undergoing SHM increases as its amplitude of oscillation increases.
False.
For small angles of oscillation, the time period of SHM is independent of the amplitude of oscillation.
Define periodic function, in the context of undamped SHM graphs.
A function that repeats itself at regular intervals. All undamped SHM graphs are periodic functions, so can be described by sine and cosine curves.
If an oscillator starts oscillating from the equilibrium position, what shape is its displacement-time graph?
A sine curve.
If an oscillator starts oscillating from the amplitude position, what shape is its displacement-time graph?
A cosine curve.
How is the velocity of an oscillator at any instant found from its displacement-time graph?
It is equal to the gradient of the displacement-time graph at that instant.
At what point in an oscillation is an oscillator's velocity at a maximum?
At the equilibrium position, where displacement x = 0.
The acceleration-time graph is a .......... of the displacement-time graph in the x-axis.
The acceleration-time graph is a reflection of the displacement-time graph in the x-axis.
At what displacement is an oscillator's acceleration at a maximum?
At its maximum displacement (the amplitude position).
True or False?
The velocity-time graph and acceleration-time graph of an oscillator in SHM are in phase with each other.
False.
The displacement, velocity and acceleration graphs of an oscillator in SHM are all 90° out of phase with each other.
Give the equation for the maximum speed of an oscillator in SHM.
$v_{m a x} = ω A$
At what point in an oscillation does an oscillator have its maximum speed?
At the equilibrium position.
Give the equation for the maximum acceleration of an oscillator in SHM.
$a_{m a x} = ω^{2} A$
At what point in an oscillation does an oscillator have its maximum acceleration?
At its maximum displacement (the amplitude position, x = A).
The acceleration of an oscillator is .......... at the equilibrium position.
The acceleration of an oscillator is zero at the equilibrium position.
True or False?
An oscillator has its maximum speed at its position of maximum displacement.
False.
Maximum speed occurs at the equilibrium position; at maximum displacement (the amplitude) the speed is zero.
Give the equation for the restoring force in a mass-spring system undergoing SHM.
$F_{H} = - k x$
What everyday physics law is the mass-spring restoring force equation, F_H = −kx, equivalent to?
Hooke's Law.
Give the equation for the time period of a mass-spring system, defining m and k.
$T = 2 π \sqrt{\frac{m}{k}}$
- m = mass on the end of the spring (kg)
- k = spring constant (N m^-1)
Does the time period of a mass-spring system depend on the gravitational field strength?
No. The equation does not include g, so the oscillations would have the same time period on Earth and the Moon.
The equation for the time period of a mass-spring system applies to both .......... and .......... mass-spring systems.
The equation for the time period of a mass-spring system applies to both horizontal and vertical mass-spring systems.
True or False?
A spring with a higher spring constant has a longer time period of oscillation.
False.
A higher spring constant makes a stiffer spring, which gives a shorter time period of oscillation.
Define a simple pendulum.
A string and bob, where the bob is a weight (generally spherical, treated as a point mass) that moves side to side. The string is light and inextensible, remains in tension throughout, and is attached to a fixed point above the equilibrium position.
Give the equation for the time period of a simple pendulum, defining L.
$T = 2 π \sqrt{\frac{L}{g}}$
L = length of string, from the pivot to the centre of mass of the bob (m)
Does the time period of a simple pendulum depend on the gravitational field strength?
Yes. Its time period would be different on the Earth and the Moon.
The time period equation for a simple pendulum is only valid for .......... angles of oscillation, where θ < 10°.
The time period equation for a simple pendulum is only valid for small angles of oscillation, where θ < 10°.
What approximation is made for sin θ when using the small angle approximation for a pendulum?
sin θ ≅ *θ*.
True or False?
For the small angle approximation, the restoring force on a pendulum bob is assumed to act vertically.
False.
It is assumed the restoring force acts horizontally, towards the equilibrium position (since sin θ ≅ θ for small angles).
Give an example of a harmonic oscillator, other than a pendulum or mass-spring system.
Liquid oscillating in a U-tube.
Give the equation for the time period of liquid oscillating in a U-tube, defining l.
$T = 2 π \sqrt{\frac{l}{g}}$
l = known length of the liquid column (m)
The time period equation for liquid oscillating in a U-tube is the same as the equation used for a ...........
The time period equation for liquid oscillating in a U-tube is the same as the equation used for a simple pendulum.
True or False?
The time period equation for a U-tube oscillator uses the total length of the U-tube.
False.
It uses l, the length of the liquid column only, not the total length of the tube.
Why does water oscillating in a U-tube undergo simple harmonic motion?
Its restoring force is proportional to its displacement from the equilibrium position, as with a spring or pendulum.
A U-tube contains a 20 cm column of water oscillating in SHM. Calculate the frequency of the oscillations.
$f = \frac{1}{2 π} \sqrt{\frac{g}{l}} = \frac{1}{2 π} \sqrt{\frac{9.81}{0.20}}$
f = 1.11 Hz
Define total energy in a simple harmonic system.
The total energy of a simple harmonic system remains constant throughout the oscillation and is equal to the sum of the kinetic and potential energy:
$E = E_{p} + E_{k}$
In a horizontal mass-spring system oscillating in SHM, at which position is the elastic potential energy maximum, and at which is it minimum?
- Maximum at the amplitude position, where the spring is fully stretched
- Minimum (zero) at the equilibrium position
In a simple pendulum oscillating in SHM, at which position is the gravitational potential energy maximum, and at which is the kinetic energy maximum?
- Gravitational potential energy is maximum at the amplitude position (top of the swing)
- Kinetic energy is maximum at the equilibrium position
State the equations used to calculate gravitational potential energy, elastic potential energy and kinetic energy in an SHM system.
- Gravitational potential energy: $E_{p} = m g h$
- Elastic potential energy: $E_{p} = \frac{1}{2} k x^{2}$
- Kinetic energy: $E_{k} = \frac{1}{2} m v^{2}$
On the energy-displacement graph for SHM, potential energy is represented by a .......... shaped curve, while kinetic energy is represented by a .......... shaped curve.
On the energy-displacement graph for SHM, potential energy is represented by a 'U' shaped curve, while kinetic energy is represented by a 'n' shaped curve.
Why does the energy-time graph for a simple pendulum in SHM never show negative values on the y-axis?
Energy is always positive, so an SHM energy-time graph drawn with negative energy values is incorrect.
True or False?
On an energy-displacement graph for SHM, the total energy is represented by a curve that peaks at the amplitude position, in the same way as the potential energy curve.
False.
The total energy is represented by a horizontal straight line above the potential and kinetic energy curves, since it remains constant throughout the oscillation.
What is the resolution of a stopwatch and a metre ruler typically used in this required practical?
- Stopwatch: ±0.01 s
- Metre ruler: ±1 mm
In the mass-spring SHM experiment used to determine the spring constant, state the independent, dependent and control variables.
- Independent variable: mass, m
- Dependent variable: time period, T
- Control variables: spring constant, k and number of oscillations
In the simple pendulum experiment used to determine acceleration due to gravity, state the independent, dependent and control variables.
- Independent variable: length, L
- Dependent variable: time period, T
- Control variables: mass of pendulum bob and number of oscillations
Why is the time for ten complete oscillations measured and then divided by ten, rather than timing a single oscillation?
To reduce the random error in the measured time period, for example the error introduced by reaction time when starting and stopping the stopwatch.
How is the spring constant, k, obtained from the results of the mass-spring SHM experiment?
- Plot a graph of $T^{2}$ (y-axis) against mass, m (x-axis)
- Gradient $= \frac{4 π^{2}}{k}$
- So $k = \frac{4 π^{2}}{gradient}$
- Compare this value with k found from the gradient of a force-extension graph (Hooke's law)
How is the acceleration due to gravity, g, obtained from the results of the simple pendulum SHM experiment?
- Plot a graph of $T^{2}$ (y-axis) against length, L (x-axis)
- Gradient $= \frac{4 π^{2}}{g}$
- So $g = \frac{4 π^{2}}{gradient}$
- Compare this value with the accepted value, g = 9.81 m s^-2
One complete oscillation of a pendulum is counted from the equilibrium position, to one .........., to the other maximum, and back to equilibrium again.
One complete oscillation of a pendulum is counted from the equilibrium position, to one maximum, to the other maximum, and back to equilibrium again.
State one systematic error and one random error precaution used in this required practical.
- Systematic: reduce parallax error by viewing the marker at eye level
- Random: keep oscillation amplitudes small, use the same starting angle or displacement each time, and repeat any pendulum readings that do not swing in a straight line
True or False?
In the pendulum required practical, one complete oscillation is counted as the pendulum swinging from one side to the other side.
False.
One complete oscillation is counted from the equilibrium position, to one maximum, to the other maximum, and back to the equilibrium position again, not just from side to side.

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