An oscillation is the repetitive variation with time t of the displacement x of an object about the equilibrium position ( x = 0).

Define displacement in the context of an oscillation.

Displacement is the distance of a point on the wave from its equilibrium position. It is a vector quantity, so it can be positive or negative.

Amplitude is the maximum value of the displacement on either side of the equilibrium position.

What does it mean for an oscillation to be isochronous ?

It means the oscillation has a constant period .

The time interval for one complete oscillation is called the .......... , measured in seconds.

The time interval for one complete oscillation is called the period , measured in seconds.

True or False? When the crest of one wave aligns with the trough of another wave of the same frequency, the two waves are in phase.

False. When a crest aligns with a trough, the waves are in antiphase (180° or π radians out of phase). Waves are only in phase when their crests or troughs are aligned.

Define angular frequency .

Angular frequency is the rate of change of angular position with respect to time.

The angular frequency of an object in simple harmonic motion is equivalent to which quantity in circular motion?

The angular speed of an object undergoing uniform circular motion.

The time taken to complete one oscillation, or revolution, is equal to the .......... , T .

The time taken to complete one oscillation, or revolution, is equal to the period , T .

True or False? Angular frequency is measured in hertz (Hz).

False. Angular frequency is measured in radians per second (rad s⁻¹) , not hertz.

Define simple harmonic motion (SHM) .

SHM is an oscillation in which the acceleration of a body is proportional to its displacement , but acts in the opposite direction .

State the two conditions required for an object to undergo simple harmonic motion.

The acceleration is proportional to the displacement, and the acceleration is in the opposite direction to the displacement.

In SHM, the acceleration is proportional to the displacement but acts in the .......... direction to it.

In SHM, the acceleration is proportional to the displacement but acts in the opposite direction to it.

True or False? A person bouncing on a trampoline is an example of simple harmonic motion.

False. While airborne, the restoring force on the person is their weight , which stays constant and is not proportional to their displacement from equilibrium, so the conditions for SHM are not met.

What does it mean for an oscillator to be isochronous ?

The period of oscillation is independent of the amplitude .

To find the spring constant of a mass-spring system, a graph of .......... against mass m is plotted, and the spring constant is found from its gradient.

To find the spring constant of a mass-spring system, a graph of T ² against mass m is plotted, and the spring constant is found from its gradient.

In the mass-spring practical, what are the independent and dependent variables?

Independent variable = mass , m . Dependent variable = time period , T .

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

False. One complete oscillation is when the pendulum passes through the equilibrium position , to one amplitude, back through equilibrium to the other amplitude, and back to equilibrium again.

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

This reduces the effect of random error (such as reaction time when starting and stopping the stopwatch) on the calculated period.

The greater the .......... of an oscillation, the greater its velocity when passing through the equilibrium position.

The greater the amplitude of an oscillation, the greater its velocity when passing through the equilibrium position.

True or False? The velocity of an oscillator in SHM is a scalar quantity.

False. Velocity is a vector quantity; it is the speed of the oscillator in a certain direction.

What type of curves describe the displacement, velocity and acceleration of an object in undamped simple harmonic motion?

Sine and cosine curves, since all undamped SHM graphs are periodic functions .

What is the phase relationship between the displacement, velocity and acceleration graphs in SHM?

They are all 90° out of phase with each other.

How are the amplitude and time period of an oscillation found from a displacement-time graph?

The amplitude A is the maximum value of x ; the time period T is the time taken for one full cycle.

How is the velocity of an oscillator at any time determined from a displacement-time graph?

Velocity is equal to the gradient of the displacement-time graph .

An oscillator moves the .......... at its equilibrium position.

An oscillator moves the fastest at its equilibrium position.

How does the acceleration-time graph relate to the displacement-time graph in SHM?

The acceleration-time graph is a reflection of the displacement-time graph in the time axis, since acceleration always acts in the opposite direction to positive displacement.

How is the acceleration of an oscillator at any time determined, and when is it at its maximum?

Acceleration is equal to the gradient of the velocity-time graph , and is at its maximum when the displacement is at its maximum .

True or False? A displacement-time graph for SHM must always start at zero displacement when t = 0.

False. The graph might not always start at zero - if the oscillation starts at the positive or negative amplitude, the displacement will be at its maximum at t = 0.

A LevelPhysicsOCRFlashcards5. Newtonian World & AstrophysicsSimple Harmonic Oscillations

Simple Harmonic Oscillations (OCR A Level Physics): Flashcards

Exam code: H556

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FrontDescribing Oscillations
Define oscillation.

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Cards in this collection (47)

Define oscillation.
An oscillation is the repetitive variation with time t of the displacement x of an object about the equilibrium position (x = 0).
Define displacement in the context of an oscillation.
Displacement is the distance of a point on the wave from its equilibrium position. It is a vector quantity, so it can be positive or negative.
Define amplitude.
Amplitude is the maximum value of the displacement on either side of the equilibrium position.
What does it mean for an oscillation to be isochronous?
It means the oscillation has a constant period.
The time interval for one complete oscillation is called the .........., measured in seconds.
The time interval for one complete oscillation is called the period, measured in seconds.
State the equation relating frequency f and period T.
$f = \frac{1}{T}$
True or False?
When the crest of one wave aligns with the trough of another wave of the same frequency, the two waves are in phase.
False.
When a crest aligns with a trough, the waves are in antiphase (180° or π radians out of phase). Waves are only in phase when their crests or troughs are aligned.
Besides fractions of a wavelength, in what two other units can phase difference be measured?
Degrees and radians.
Define angular frequency.
Angular frequency is the rate of change of angular position with respect to time.
State the equation linking angular frequency ω to the time period T and frequency f.
$ω = \frac{2 π}{T} = 2 π f$
The angular frequency of an object in simple harmonic motion is equivalent to which quantity in circular motion?
The angular speed of an object undergoing uniform circular motion.
The time taken to complete one oscillation, or revolution, is equal to the .........., T.
The time taken to complete one oscillation, or revolution, is equal to the period, T.
True or False?
Angular frequency is measured in hertz (Hz).
False.
Angular frequency is measured in radians per second (rad s⁻¹), not hertz.
In the equation $ω = \frac{2 π}{T}$ , what does the $2 π$ represent?
The circumference of a circle (in radians), corresponding to one complete revolution.
Define simple harmonic motion (SHM).
SHM is an oscillation in which the acceleration of a body is proportional to its displacement, but acts in the opposite direction.
State the defining equation of SHM relating acceleration a and displacement x.
$a \propto - x$
State the two conditions required for an object to undergo simple harmonic motion.
The acceleration is proportional to the displacement, and the acceleration is in the opposite direction to the displacement.
In SHM, the acceleration is proportional to the displacement but acts in the .......... direction to it.
In SHM, the acceleration is proportional to the displacement but acts in the opposite direction to it.
True or False?
A person bouncing on a trampoline is an example of simple harmonic motion.
False.
While airborne, the restoring force on the person is their weight, which stays constant and is not proportional to their displacement from equilibrium, so the conditions for SHM are not met.
What does it mean for an oscillator to be isochronous?
The period of oscillation is independent of the amplitude.
State the equation for the time period of a mass-spring system.
$T = 2 π \sqrt{\frac{m}{k}}$ where m = mass (kg) and k = spring constant (N m⁻¹).
State the equation for the time period of a simple pendulum.
$T = 2 π \sqrt{\frac{L}{g}}$ where L = length of the pendulum (m) and g = acceleration due to gravity (m s⁻²).
To find the spring constant of a mass-spring system, a graph of .......... against mass m is plotted, and the spring constant is found from its gradient.
To find the spring constant of a mass-spring system, a graph of T² against mass m is plotted, and the spring constant is found from its gradient.
In the mass-spring practical, what are the independent and dependent variables?
Independent variable = mass, m. Dependent variable = time period, T.
True or False?
In the simple pendulum practical, one complete oscillation is measured as the pendulum swinging from one side to the other side only.
False.
One complete oscillation is when the pendulum passes through the equilibrium position, to one amplitude, back through equilibrium to the other amplitude, and back to equilibrium again.
Why is the time for ten oscillations measured and then divided by ten, rather than timing a single oscillation?
This reduces the effect of random error (such as reaction time when starting and stopping the stopwatch) on the calculated period.
State the equation for the acceleration a of an object in SHM in terms of angular frequency ω and displacement x.
$a = - ω^{2} x$
At what displacement does an oscillator in SHM experience its maximum acceleration?
At maximum displacement, i.e. when $x = x_{0}$ (the amplitude).
What does the minus sign in $a = - ω^{2} x$ indicate?
The acceleration is always directed in the opposite direction to the displacement, i.e. back towards the equilibrium position.
On a graph of acceleration against displacement for an object in SHM, the gradient is equal to ...........
On a graph of acceleration against displacement for an object in SHM, the gradient is equal to $- ω^{2}$ .
Which displacement equation applies when an object begins oscillating from the equilibrium position ( $x = 0$ at $t = 0$ )?
$x = x_{0} \sin ω t$
Which displacement equation applies when an object begins oscillating from its amplitude position ( $x = \pm x_{0}$ at $t = 0$ )?
$x = x_{0} \cos ω t$
True or False?
The graph of acceleration against displacement for an object in SHM is a straight line with a positive gradient.
False.
Since $a = - ω^{2} x$ , the graph is a straight line through the origin with a negative gradient, sloping downwards.
At what point in an oscillation does an object in SHM have its maximum velocity?
At the equilibrium position, i.e. when its displacement is zero ( $x = 0$ ).
State the equation for the velocity v of an oscillator starting from the equilibrium position, in terms of maximum velocity $v_{0}$ , angular frequency ω and time t.
$v = v_{0} \cos ω t$
State the equation relating velocity v to displacement x, amplitude $x_{0}$ and angular frequency ω.
$v = \pm ω \sqrt{x_{0}^{2} - x^{2}}$
State the equation for the maximum velocity $v_{0}$ of an oscillator.
$v_{0} = ω x_{0}$
The greater the .......... of an oscillation, the greater its velocity when passing through the equilibrium position.
The greater the amplitude of an oscillation, the greater its velocity when passing through the equilibrium position.
True or False?
The velocity of an oscillator in SHM is a scalar quantity.
False.
Velocity is a vector quantity; it is the speed of the oscillator in a certain direction.
What type of curves describe the displacement, velocity and acceleration of an object in undamped simple harmonic motion?
Sine and cosine curves, since all undamped SHM graphs are periodic functions.
What is the phase relationship between the displacement, velocity and acceleration graphs in SHM?
They are all 90° out of phase with each other.
How are the amplitude and time period of an oscillation found from a displacement-time graph?
The amplitude A is the maximum value of x; the time period T is the time taken for one full cycle.
How is the velocity of an oscillator at any time determined from a displacement-time graph?
Velocity is equal to the gradient of the displacement-time graph.
An oscillator moves the .......... at its equilibrium position.
An oscillator moves the fastest at its equilibrium position.
How does the acceleration-time graph relate to the displacement-time graph in SHM?
The acceleration-time graph is a reflection of the displacement-time graph in the time axis, since acceleration always acts in the opposite direction to positive displacement.
How is the acceleration of an oscillator at any time determined, and when is it at its maximum?
Acceleration is equal to the gradient of the velocity-time graph, and is at its maximum when the displacement is at its maximum.
True or False?
A displacement-time graph for SHM must always start at zero displacement when t = 0.
False.
The graph might not always start at zero - if the oscillation starts at the positive or negative amplitude, the displacement will be at its maximum at t = 0.

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