Define simple harmonic motion (SHM) .

An oscillation in which the acceleration is proportional to the displacement and always directed opposite to the displacement (towards the equilibrium position).

State the two conditions for an oscillation to be simple harmonic motion.

The acceleration is proportional to the displacement The acceleration is in the opposite direction to the displacement (towards equilibrium)

Define restoring force .

The force that always acts to return an oscillating object to its equilibrium position , and is proportional to the displacement from that position.

In SHM the restoring force is always proportional to the displacement and directed back towards the .......... position.

In SHM the restoring force is always proportional to the displacement and directed back towards the equilibrium position.

True or False? A person jumping on a trampoline undergoes SHM.

False. The restoring force is not proportional to displacement . While airborne the restoring force equals the person's weight , which is constant and does not change even if they jump higher.

Give three examples of oscillators that undergo simple harmonic motion.

Any from: the pendulum of a clock a mass on a spring guitar strings the electrons in alternating current in a wire

In SHM, where is the speed greatest and where is the acceleration greatest?

Speed is greatest at the equilibrium position ( x = 0) Acceleration is greatest at maximum displacement ( x = A )

What does the gradient of an acceleration–displacement graph for SHM equal?

The gradient equals −ω 2 — the graph is a straight line through the origin sloping downwards, with maximum and minimum x at the amplitudes −A and +A .

True or False? An oscillator's speed is greatest at maximum displacement.

False. Speed is greatest at the equilibrium position ( x = 0) and is zero at maximum displacement ( x = A ).

Define simple pendulum .

An object (bob) that swings from side to side , attached to a fixed point above it.

In the pendulum period equation, l is the .......... of the pendulum swing and g is the gravitational field strength.

In the pendulum period equation, l is the length of the pendulum swing and g is the gravitational field strength.

Describe an experimental method to observe the motion of a mass-spring system .

attach a pencil to the mass and set it in free oscillation by displacing it downwards pull a sheet of graph paper sideways as the mass oscillates so the pencil traces the motion this gives a periodic curve whose amplitude decreases as the system slows

How is the amplitude found from a displacement–time graph?

From the maximum value of the displacement x .

How is the time period found from a displacement–time graph?

By reading the time taken for one full cycle (one complete oscillation).

All undamped SHM displacement–time graphs are periodic functions and can be described by .......... curves.

All undamped SHM displacement–time graphs are periodic functions and can be described by sine and cosine curves.

What determines whether a displacement–time graph starts at zero or at maximum displacement?

The starting position at t = 0 : starts at maximum if the object begins at its amplitude starts at zero if the object begins at the equilibrium position

True or False? An SHM displacement–time graph must always start at zero.

False. The graph may start at the positive or negative amplitude depending on where the object is at t = 0 — it does not have to start at zero displacement.

What is the phase relationship between the velocity–time and displacement–time graphs in SHM?

They are 90° out of phase with each other.

How can the velocity of an oscillator be found from a displacement–time graph?

Velocity is the rate of change of displacement , so it equals the gradient of the displacement–time graph at any point.

The velocity of an oscillator is at its maximum when its displacement is .......... .

The velocity of an oscillator is at its maximum when its displacement is zero (at the equilibrium position).

True or False? An oscillator's velocity is greatest at maximum displacement.

False. Velocity is greatest at zero displacement (the equilibrium position), where the oscillator moves fastest, and is zero at maximum displacement .

What shape is an undamped velocity–time graph, and does its exact appearance depend on the starting position?

It is always a general sine or cosine curve . The exact appearance depends on where the object starts at t = 0 , but with no damping it is always sinusoidal.

A LevelPhysicsEdexcelFlashcards13. OscillationsSimple Harmonic Motion

Simple Harmonic Motion (Edexcel A Level Physics): Flashcards

Exam code: 9PH0

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FrontConditions for Simple Harmonic Motion
Define simple harmonic motion (SHM).
FrontConditions for Simple Harmonic Motion
State the two conditions for an oscillation to be simple harmonic motion.
BackConditions for Simple Harmonic Motion
The acceleration is proportional to the displacement
The acceleration is in the opposite direction to the displacement (towards equilibrium)

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Cards in this collection (31)

Define simple harmonic motion (SHM).
An oscillation in which the acceleration is proportional to the displacement and always directed opposite to the displacement (towards the equilibrium position).
State the two conditions for an oscillation to be simple harmonic motion.
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement (towards equilibrium)
Define restoring force.
The force that always acts to return an oscillating object to its equilibrium position, and is proportional to the displacement from that position.
In SHM the restoring force is always proportional to the displacement and directed back towards the .......... position.
In SHM the restoring force is always proportional to the displacement and directed back towards the equilibrium position.
In the restoring force equation $F = - k x$ , what is the significance of the minus sign?
It shows the restoring force (and acceleration) always acts towards the equilibrium position — in the opposite direction to the displacement x.
True or False?
A person jumping on a trampoline undergoes SHM.
False.
The restoring force is not proportional to displacement. While airborne the restoring force equals the person's weight, which is constant and does not change even if they jump higher.
Give three examples of oscillators that undergo simple harmonic motion.
Any from:
- the pendulum of a clock
- a mass on a spring
- guitar strings
- the electrons in alternating current in a wire
State the equation for the acceleration of an object in SHM.
$a = - ω^{2} x$
where a = acceleration (m s^-2), ω = angular frequency (rad s^-1) and x = displacement (m).
The minus sign in $a = - ω^{2} x$ shows that the acceleration and displacement always act in .......... directions.
The minus sign in $a = - ω^{2} x$ shows that the acceleration and displacement always act in opposite directions.
When is the SHM displacement equation written as $x = A \cos (ω t)$ and when as $x = A \sin (ω t)$ ?
- Cosine — when the object starts at its amplitude (x = A at t = 0)
- Sine — when the object starts at its equilibrium position (x = 0 at t = 0)
State the equation for the speed of an oscillator at displacement x.
$v = \pm ω \sqrt{A^{2} - x^{2}}$
where v = speed (m s^-1), A = amplitude (m), ω = angular frequency (rad s^-1) and x = displacement (m).
In SHM, where is the speed greatest and where is the acceleration greatest?
- Speed is greatest at the equilibrium position (x = 0)
- Acceleration is greatest at maximum displacement (x = A)
What does the gradient of an acceleration–displacement graph for SHM equal?
The gradient equals −ω² — the graph is a straight line through the origin sloping downwards, with maximum and minimum x at the amplitudes −A and +A.
True or False?
An oscillator's speed is greatest at maximum displacement.
False.
Speed is greatest at the equilibrium position (x = 0) and is zero at maximum displacement (x = A).
State the equation for the period of a simple pendulum.
$T = 2 π \sqrt{\frac{l}{g}}$
where l is the length of the pendulum and g is the gravitational field strength.
State the equation for the period of a mass-spring system.
$T = 2 π \sqrt{\frac{m}{k}}$
where m is the mass on the spring and k is the spring constant.
Define simple pendulum.
An object (bob) that swings from side to side, attached to a fixed point above it.
In the pendulum period equation, l is the .......... of the pendulum swing and g is the gravitational field strength.
In the pendulum period equation, l is the length of the pendulum swing and g is the gravitational field strength.
Which two quantities determine the period of a mass-spring system?
- the mass m on the end of the spring
- the spring constant k
The restoring force $F = - k x$ is the same form as Hooke's law.
Describe an experimental method to observe the motion of a mass-spring system.
- attach a pencil to the mass and set it in free oscillation by displacing it downwards
- pull a sheet of graph paper sideways as the mass oscillates so the pencil traces the motion
- this gives a periodic curve whose amplitude decreases as the system slows
True or False?
The period of a simple pendulum depends on the mass of the bob.
False.
From $T = 2 π \sqrt{\frac{l}{g}}$ the period depends only on the length l and gravitational field strength g — not on the mass of the bob.
How is the amplitude found from a displacement–time graph?
From the maximum value of the displacement x.
How is the time period found from a displacement–time graph?
By reading the time taken for one full cycle (one complete oscillation).
All undamped SHM displacement–time graphs are periodic functions and can be described by .......... curves.
All undamped SHM displacement–time graphs are periodic functions and can be described by sine and cosine curves.
What determines whether a displacement–time graph starts at zero or at maximum displacement?
The starting position at t = 0:
- starts at maximum if the object begins at its amplitude
- starts at zero if the object begins at the equilibrium position
True or False?
An SHM displacement–time graph must always start at zero.
False.
The graph may start at the positive or negative amplitude depending on where the object is at t = 0 — it does not have to start at zero displacement.
What is the phase relationship between the velocity–time and displacement–time graphs in SHM?
They are 90° out of phase with each other.
How can the velocity of an oscillator be found from a displacement–time graph?
Velocity is the rate of change of displacement, so it equals the gradient of the displacement–time graph at any point.
The velocity of an oscillator is at its maximum when its displacement is ...........
The velocity of an oscillator is at its maximum when its displacement is zero (at the equilibrium position).
True or False?
An oscillator's velocity is greatest at maximum displacement.
False.
Velocity is greatest at zero displacement (the equilibrium position), where the oscillator moves fastest, and is zero at maximum displacement.
What shape is an undamped velocity–time graph, and does its exact appearance depend on the starting position?
It is always a general sine or cosine curve. The exact appearance depends on where the object starts at t = 0, but with no damping it is always sinusoidal.

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