Define simple harmonic motion (SHM) .

An oscillation in which the acceleration is directly proportional to the displacement from equilibrium, and always acts in the opposite direction to the displacement.

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

The acceleration is proportional to the displacement The acceleration is in the opposite direction to the displacement

Give four examples of oscillators that undergo simple harmonic motion.

The pendulum of a clock A mass on a spring Guitar strings Electrons in alternating current flowing through a wire

True or False? A person bouncing on a trampoline is performing simple harmonic motion.

False. While airborne, the restoring force on the person is equal to their weight , which is constant rather than proportional to their displacement from the equilibrium position, so the motion is not SHM.

Define amplitude ( A ) in SHM.

The maximum displacement of an oscillator from its equilibrium position.

When calculating displacement or speed in SHM using sine or cosine functions, your calculator must be in .......... mode, not degrees.

When calculating displacement or speed in SHM using sine or cosine functions, your calculator must be in radians mode, not degrees.

Define a simple pendulum .

An object moving from side to side, attached to a string which is fixed to a point above.

Define a mass-spring system .

An object moving up and down, or side to side, attached to the end of a spring.

In the period equation for a simple pendulum, what do l and g represent?

l = the length of the pendulum g = the gravitational field strength on the planet the pendulum is set up on

When a pencil traces the motion of an oscillating mass-spring system on graph paper, the curve produced will .......... in amplitude as the system slows down.

When a pencil traces the motion of an oscillating mass-spring system on graph paper, the curve produced will decrease in amplitude as the system slows down.

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

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

How is the amplitude of an oscillation determined from a displacement-time graph?

From the maximum value of x (the peak displacement) on the graph.

How is the period of an oscillation determined from a displacement-time graph?

By reading the time taken for one full cycle of the graph.

What shape do all undamped SHM displacement-time graphs take, regardless of where the oscillator starts at t = 0?

A general sine or cosine curve .

True or False? A displacement-time graph for an oscillator undergoing SHM must always start at zero displacement.

False. The graph can start at any displacement value depending on where the object begins oscillating at t = 0 — it could start at zero, or at the positive/negative amplitude.

How can the velocity of an SHM oscillator at a given instant be determined from its displacement-time graph?

From the gradient of the displacement-time graph at that instant.

At what point in its oscillation does an SHM oscillator move fastest, and why?

At the equilibrium position ( x = 0), because velocity is at its maximum when displacement is zero.

What shape does an undamped SHM velocity-time graph take?

A general sine or cosine curve — the same family of curve as the displacement-time graph, but 90 o out of phase with it.

True or False? An oscillator undergoing SHM has zero velocity at its equilibrium position.

False. Velocity is at its maximum at the equilibrium position; it is zero at the amplitude positions ( x = ± A ).

The velocity-time graph for an oscillator in SHM is 90 o out of phase with the .......... -time graph.

The velocity-time graph for an oscillator in SHM is 90 o out of phase with the displacement -time graph.

International A Level (IAL)PhysicsEdexcelFlashcards5. Thermodynamics, Radiation, Oscillations & CosmologySimple Harmonic Motion

Simple Harmonic Motion (Edexcel International A Level (IAL) Physics): Flashcards

Exam code: YPH11

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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 classed as 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

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Cards in this collection (30)

Define simple harmonic motion (SHM).
An oscillation in which the acceleration is directly proportional to the displacement from equilibrium, and always acts in the opposite direction to the displacement.
Define restoring force.
A force that always acts to return an oscillator to its equilibrium position, given by $F = - k x$
State the two conditions for an oscillation to be classed as simple harmonic motion.
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement
Give four examples of oscillators that undergo simple harmonic motion.
- The pendulum of a clock
- A mass on a spring
- Guitar strings
- Electrons in alternating current flowing through a wire
True or False?
A person bouncing on a trampoline is performing simple harmonic motion.
False.
While airborne, the restoring force on the person is equal to their weight, which is constant rather than proportional to their displacement from the equilibrium position, so the motion is not SHM.
In the equation $F = - k x$ , the negative sign shows that the restoring force always acts towards the .......... of oscillation.
In the equation $F = - k x$ , the negative sign shows that the restoring force always acts towards the centre of oscillation.
Define amplitude (A) in SHM.
The maximum displacement of an oscillator from its equilibrium position.
Define angular frequency (⍵), and state how it relates to the time period.
The rate of change of angular displacement, measured in rad s^-1. It is related to the time period T by $ω = \frac{2 π}{T}$
State the SHM acceleration equation and explain what the negative sign shows about the direction of acceleration.
$a = - ω^{2} x$
The negative sign shows that acceleration is always directed opposite to the displacement, i.e. towards the equilibrium position.
Which SHM displacement equation, x = Acos(⍵t) or x = Asin(⍵t), applies when an oscillator is released from its amplitude position, and which applies when it starts at the equilibrium position?
- Released from amplitude (x = A at t = 0): $x = A \cos (ω t)$
- Starts at equilibrium (x = 0 at t = 0): $x = A \sin (ω t)$
State the equation relating the speed of an SHM oscillator to its angular frequency, amplitude and displacement.
$v = \pm ω \sqrt{A^{2} - x^{2}}$
True or False?
An oscillator undergoing SHM has its greatest speed at its amplitude position.
False.
The greatest speed occurs at the equilibrium position (x = 0); using $v = \pm ω \sqrt{A^{2} - x^{2}}$ , speed is zero when x = A.
When calculating displacement or speed in SHM using sine or cosine functions, your calculator must be in .......... mode, not degrees.
When calculating displacement or speed in SHM using sine or cosine functions, your calculator must be in radians mode, not degrees.
Define a simple pendulum.
An object moving from side to side, attached to a string which is fixed to a point above.
Define a mass-spring system.
An object moving up and down, or side to side, attached to the end of a spring.
State the equation for the period of a simple pendulum.
$T = 2 π \sqrt{\frac{l}{g}}$
In the period equation for a simple pendulum, what do l and g represent?
- l = the length of the pendulum
- g = the gravitational field strength on the planet the pendulum is set up on
State the equation for the period of a mass-spring system.
$T = 2 π \sqrt{\frac{m}{k}}$
True or False?
Increasing the mass on the end of a spring decreases its period of oscillation.
False.
Increasing the mass increases the period, since $T = 2 π \sqrt{\frac{m}{k}}$ shows T is proportional to the square root of m.
When a pencil traces the motion of an oscillating mass-spring system on graph paper, the curve produced will .......... in amplitude as the system slows down.
When a pencil traces the motion of an oscillating mass-spring system on graph paper, the curve produced will decrease in amplitude as the system slows down.
Define a periodic function, in the context of undamped SHM graphs.
A function that repeats itself at regular intervals. All undamped SHM displacement-time graphs are periodic functions and can be described by sine or cosine curves.
How is the amplitude of an oscillation determined from a displacement-time graph?
From the maximum value of x (the peak displacement) on the graph.
How is the period of an oscillation determined from a displacement-time graph?
By reading the time taken for one full cycle of the graph.
What shape do all undamped SHM displacement-time graphs take, regardless of where the oscillator starts at t = 0?
A general sine or cosine curve.
True or False?
A displacement-time graph for an oscillator undergoing SHM must always start at zero displacement.
False.
The graph can start at any displacement value depending on where the object begins oscillating at t = 0 — it could start at zero, or at the positive/negative amplitude.
How can the velocity of an SHM oscillator at a given instant be determined from its displacement-time graph?
From the gradient of the displacement-time graph at that instant.
At what point in its oscillation does an SHM oscillator move fastest, and why?
At the equilibrium position (x = 0), because velocity is at its maximum when displacement is zero.
What shape does an undamped SHM velocity-time graph take?
A general sine or cosine curve — the same family of curve as the displacement-time graph, but 90^o out of phase with it.
True or False?
An oscillator undergoing SHM has zero velocity at its equilibrium position.
False.
Velocity is at its maximum at the equilibrium position; it is zero at the amplitude positions (x = ±A).
The velocity-time graph for an oscillator in SHM is 90^o out of phase with the ..........-time graph.
The velocity-time graph for an oscillator in SHM is 90^o out of phase with the displacement-time graph.

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