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

Define equilibrium position .

The equilibrium position ( x = 0) is the position at which there is no resultant force acting on the object.

The amplitude ( x 0 ) is the maximum value of the displacement on either side of the equilibrium position, measured in metres.

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

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

True or False? Displacement is a scalar quantity that is always positive.

False. Displacement is a vector quantity — it can be positive or negative depending on which side of the equilibrium position the object is on.

Define simple harmonic motion (SHM).

Simple harmonic motion is an oscillation in which the acceleration is proportional to the displacement from a fixed point and is always directed towards that point (opposite in direction to the displacement).

Give three examples of oscillators that undergo simple harmonic motion.

A pendulum A mass on a spring A guitar string vibrating A ruler vibrating off the end of a table A child on a swing

Explain why a person jumping on a trampoline is not an example of simple harmonic motion.

The restoring force is not proportional to the person's displacement. While not in contact with the trampoline, the restoring force equals their weight , which stays constant even if they jump higher.

In SHM, the restoring force is always directed towards the .......... position.

In SHM, the restoring force is always directed towards the equilibrium position.

True or False? The restoring force in SHM is proportional to the object's velocity.

False. The restoring force in SHM is proportional to the object's displacement , not its velocity.

What does the negative sign in the equation a = − ω ² x indicate?

Acceleration and displacement are always in opposite directions — when the object is displaced to one side, the acceleration acts towards the equilibrium position.

On a graph of acceleration against displacement for an object in SHM, what is the gradient of the line?

The gradient is equal to − ω ² .

The displacement of an SHM oscillator reaches its maximum value, x = x 0 , when sin( ωt ) equals .......... .

The displacement of an SHM oscillator reaches its maximum value, x = x 0 , when sin( ωt ) equals 1 or −1 .

True or False? Acceleration in SHM is at its maximum value when the object's displacement is zero.

False. Acceleration is at its maximum when displacement is at its maximum ( x = x 0 ); it is speed , not acceleration, that is greatest when displacement is zero.

At what position does an oscillator in SHM reach its maximum speed?

The equilibrium position ( x = 0).

The speed of an oscillator is the .......... of its velocity.

The speed of an oscillator is the magnitude of its velocity.

True or False? For a given angular frequency, an oscillator with a greater amplitude has a greater maximum speed.

True. Since v 0 = ωx 0 , increasing the amplitude x 0 increases the maximum speed v 0 proportionally.

Define amplitude for a simple harmonic motion displacement-time graph.

The amplitude ( A ) is the maximum value of the displacement, x .

At what displacement is the velocity of an SHM oscillator at its maximum?

At the equilibrium position , where displacement x = 0.

At what displacement is the acceleration of an SHM oscillator at its maximum?

At maximum displacement (the amplitude position).

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

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

True or False? The velocity-time graph of an SHM oscillator starting from the equilibrium position is a sine curve.

False. The velocity-time graph is a cosine curve , 90° out of phase with the sine-curve displacement-time graph.

A LevelPhysicsCambridge (CIE)Flashcards17. OscillationsSimple Harmonic Oscillations

Simple Harmonic Oscillations (Cambridge (CIE) A Level Physics): Flashcards

Exam code: 9702

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FrontDescribing Oscillations
Define oscillation.

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Cards in this collection (32)

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 equilibrium position.
The equilibrium position (x = 0) is the position at which there is no resultant force acting on the object.
Define amplitude.
The amplitude (x₀) is the maximum value of the displacement on either side of the equilibrium position, measured in metres.
How does the time period T relate to frequency f and angular frequency ω?
$T = \frac{1}{f}$
$T = \frac{2 π}{ω}$
Angular frequency is the rate of change of .......... with respect to time.
Angular frequency is the rate of change of angular displacement with respect to time.
What is the phase difference, in degrees and radians, between two oscillators that are in antiphase?
180° or π radians
True or False?
Displacement is a scalar quantity that is always positive.
False.
Displacement is a vector quantity — it can be positive or negative depending on which side of the equilibrium position the object is on.
Define simple harmonic motion (SHM).
Simple harmonic motion is an oscillation in which the acceleration is proportional to the displacement from a fixed point and is always directed towards that point (opposite in direction to the displacement).
State the proportionality relationship between acceleration a and displacement x for an object undergoing SHM.
$a \propto - x$
Give three examples of oscillators that undergo simple harmonic motion.
- A pendulum
- A mass on a spring
- A guitar string vibrating
- A ruler vibrating off the end of a table
- A child on a swing
Explain why a person jumping on a trampoline is not an example of simple harmonic motion.
The restoring force is not proportional to the person's displacement. While not in contact with the trampoline, the restoring force equals their weight, which stays constant even if they jump higher.
In SHM, the restoring force is always directed towards the .......... position.
In SHM, the restoring force is always directed towards the equilibrium position.
True or False?
The restoring force in SHM is proportional to the object's velocity.
False.
The restoring force in SHM is proportional to the object's displacement, not its velocity.
State the equation for the acceleration a of an object in SHM in terms of angular frequency ω and displacement x.
$a = - ω^{2} x$
What does the negative sign in the equation a = −ω²x indicate?
Acceleration and displacement are always in opposite directions — when the object is displaced to one side, the acceleration acts towards the equilibrium position.
For an object beginning its oscillation from the equilibrium position (x = 0 at t = 0), state the equation for its displacement x.
$x = x_{0} \sin (ω t)$
On a graph of acceleration against displacement for an object in SHM, what is the gradient of the line?
The gradient is equal to −ω².
The displacement of an SHM oscillator reaches its maximum value, x = x₀, when sin(ωt) equals ...........
The displacement of an SHM oscillator reaches its maximum value, x = x₀, when sin(ωt) equals 1 or −1.
True or False?
Acceleration in SHM is at its maximum value when the object's displacement is zero.
False.
Acceleration is at its maximum when displacement is at its maximum (x = x₀); it is speed, not acceleration, that is greatest when displacement is zero.
State the equation for the speed v of an oscillator released from the equilibrium position, in terms of maximum speed v₀, angular frequency ω, and time t.
$v = v_{0} \cos (ω t)$
State the equation relating speed v to angular frequency ω, amplitude x₀ and displacement x for an oscillator in SHM.
$v = \pm ω \sqrt{(x_{0})^{2} - x^{2}}$
At what position does an oscillator in SHM reach its maximum speed?
The equilibrium position (x = 0).
State the equation for the maximum speed v₀ of an oscillator in terms of angular frequency ω and amplitude x₀.
$v_{0} = ω x_{0}$
The speed of an oscillator is the .......... of its velocity.
The speed of an oscillator is the magnitude of its velocity.
True or False?
For a given angular frequency, an oscillator with a greater amplitude has a greater maximum speed.
True.
Since v₀ = ωx₀, increasing the amplitude x₀ increases the maximum speed v₀ proportionally.
Define amplitude for a simple harmonic motion displacement-time graph.
The amplitude (A) is the maximum value of the displacement, x.
What shape is the displacement-time graph of an SHM oscillator starting from the equilibrium position?
A sine curve.
At what displacement is the velocity of an SHM oscillator at its maximum?
At the equilibrium position, where displacement x = 0.
At what displacement is the acceleration of an SHM oscillator at its maximum?
At maximum displacement (the amplitude position).
The acceleration-time graph of an SHM oscillator is a .......... of the displacement-time graph in the x-axis.
The acceleration-time graph of an SHM oscillator is a reflection of the displacement-time graph in the x-axis.
By how many degrees out of phase are the displacement-time and velocity-time graphs of an SHM oscillator?
90° out of phase.
True or False?
The velocity-time graph of an SHM oscillator starting from the equilibrium position is a sine curve.
False.
The velocity-time graph is a cosine curve, 90° out of phase with the sine-curve displacement-time graph.

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