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module 5- newtonian world and astrophysics > 5.3 Oscillations > Flashcards

5.3 Oscillations Flashcards

1
Q

What is displacement?

A

Displacement is the distance from its equilibrium position; may be positive or negative.

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2
Q

What is amplitude?

A

Amplitude is the maximum displacement and will always be positive.

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3
Q

What is frequency?

A

Number of oscillations per unit time, at any point.

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4
Q

What is the period?

A

The period is the time taken for one complete pattern of oscilllation at any point.

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5
Q

What isc the angluar frequency?

A

The angular frequency is the product of 2πf or ω=2π/T; this has units of radians per second.

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6
Q

What is phase difference?

A

The fraction of a complete cycle or oscillatio between 2 oscillating points, expressed in degrees or radians.

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7
Q

When does simple harmonic motion occur?

A

SHM occurs when the force acting on the oscillator is proportional to the displacemnt of the oscillator from some equilibrium position (x=0), amd is alawys directed back towards the equilibrium position.

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8
Q

What are the 2 ways we can calculate phase difference?

A
  • phase difference = (distance between the 2 points/ wavelength of the wave) x2π
  • Phase difference = (time between 2 points/ time period of the wave) x2π
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9
Q

At what displacement, will a spring experience a maximum resultant force?

A

Maximum displacement.

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10
Q

At what dispacement will an object experience maximum velocity on a spring?

A

0 displacement.

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11
Q

What sort of wave will simple harmonic produce against time?

A

A sinosodial wave.

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12
Q

What is simple harmonic motion?

A

If a body oscillates with SHM, it’s acceleration is directly proportional to its displacent from it’s eqilibrium position and is always directed towards that point.

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13
Q

What is constant about a body oscillating with SHM?

A

They have constant amplitude and time period.

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14
Q

IF a body is oscillating with SHM, what is its displacement directly proportional to?

A

Acceleration

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15
Q

If a body is moving in SHM, the acceleration is directly proportional to the displacement of the body from it’s equilibrium position and is alyways directed back to this point. How can this be written in an equation?

A

a = -kx
(Negative sign is present to show that the acceleration is always in the opposit direction to the displacement)

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16
Q

A body is oscillating is SHM, as its displacement increases, what direction is it’s acceleration increasing?

A

The opposite direction.

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17
Q

What are some characteristics of SHM

A
  • Velocity changes smoothly and is symetric each side of the position of equlibrium.
  • Zero velocity at maximum displacement.
  • Mazimum acceleration at maximum displacement.
  • Maximum velocity when passing through the mean or equilibrium position.
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18
Q

What equation can we use to find displacement when the timing of the simple harmonic motion starts from a point when the pendulum is released from maximum displacement?

A

x= Acosωt

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19
Q

What equation can we use to find displacement when the timing of the simple harmonic motion starts from a point when the pendulum is released from 0 displacement?

A

x= Asinsinωt

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20
Q

What does isochronous mean?

A

This means that it is constant and independent of the amplitide of the oscillation- the period of an object with simple harmonic motion is isochronous.

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21
Q

What will the dicplacement-time graph look like of an object released at amplitude performing simple harmonic motion?

A
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22
Q

How do we find the velocity from a displacement time graph?

A

Velocity is equal to the gradient of thias graph.

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23
Q

What will the velocity-time graph look like of an object released at amplitude performing simple harmonic motion?

A
24
Q

How do you find a acceleration time graph from a velocity time graph?

A

The acceleration time graph is found by plotting the values of the rate of change of velocity (the gradient of the velocity time graph at each point) against time.

25
Q

What will the acceleration-time graph look like of an object released at amplitude performing simple harmonic motion?

A

Plot of the gradient of the velocity time graph.

26
Q

What does it mean that the time period for shm is isochronous?

A

The time period is independent of its amilptude.

27
Q

What must be true for an object travalling in shm?

A

For a pendulum to oscillate with shm the angle in which it oscillates must be small?

28
Q

Ananlysing a displacement time graph of an object traveeling in shm, what can you find is true?

A

The dispacement x varies as x=A cos ωt when timing starts from almplitude. If timing starts at the point that the body passes through the equlibrium position then this will be x = A sin ωt.

29
Q

Analysing a velocity time graph of an object travelling in shm, what can you tell is true?

A

The velocity varies as v = - ωA sin ωt or as v = ωA cos ωt.

30
Q

Analysing an acceleration time graph of an object travelling in shm, what can you tell is true?

A

The acceleration varies as a= - ω^2x

31
Q

Analysing thez relationship between a siaplacemnt time graph and an accekeration time graph of an object travelling in shm, what is true?

A

The phase difference between the displacemnt and acceleration graphs is 180° or π rad.

32
Q

In shm, what is acceleration proportional to?

A

Negative displacemnt.

33
Q

When do free oscillations occur?

A

Free oscillations occur when there is no external, periodic force. The system oscillates at it’s natural frequency.

34
Q

What is natural frequency?

A

The frequency at which a system will oscillate when undergoing free oscillations.

35
Q

When do forced oscillations occur?

A

Forced oscillations occur when an external force or driving force is applied to keep a body oscillating. The system oscillates at the frequency of the driving force that is causing the oscillation.

36
Q

What is a driving frequency?

A

The frequency of the driving force applied to an oscillating object.

37
Q

Define resonance.

A

Resonance is forced oscillations occur when the driving frequency is **equal **to the natural frequency of the system being forced to oscillate . This results in the body odcillating at it’s natural frequency and maxiumum amplitude.

38
Q

What sort of frequency will occur during free oscillations?

A

Natural frequency

39
Q

What sort of frequency will occur during forced oscillation?

A

Driving frequency.

40
Q

What sort of oscillation is occuring if a system is subject to a periodic force?

A

Forced oscillations

41
Q

What are 3 examples of free oscillations?

A
  • A pendulum swinging
  • A mass-spring system
  • A fishing float bobbing on the surface of the water
42
Q

What are 3 examples of forces oscillations?

A
  • Someone being continually pushed on a swing.
  • A building vibrating during an earthquake.
  • The beating of a humming bird’s wings.
43
Q

For a forced oscillation what must be present?

A
  • A periodic force
  • 2 objects that are vibrating
44
Q

During forced oscillations, what is the frequency of the first vibrating object called?

A

Driving frequency

45
Q

When will resonance occur?

A

During forced oscillations, when the driving frquency = the natural frequency.

46
Q

What will happen to an oscillation during resonance?

A

Body will oscillate at it’s natural frequency at it’s maximum amplitude.

47
Q

What is the phase difference between the driving frequency and the natural frequency when resonance is occuring?

A

1/4 time period difference or 90°

48
Q

What famous example is used to show the conditions which resonance will occur?

A

Barton’s pendulums

49
Q

How do you set up Barton’s pendulum?

A
  • The heavy mass is pulled towards you, onced releseased, the ball will perform free oscillations and will oscillate at its natural frequency.
  • The ball is attatched to several other small balls via a length of string- as the heavy ball swings back and forward, energy ois transferred along thee string to the other balls which also start to swing in and out.
50
Q

What determines the natural frequency of Bartons pendulum?

A

The pendulums length.

51
Q

On Barton’s pendulum, which ball will oscillate with the greatest amplitude?

A

The ball on the string the same length of the driver pendulum will perform oscillations with the greatest amplitude. You would also notice this ball has π/2 cycle difference than the driver pendulum. (resonance)

52
Q

What does a graph showing how the amplitude of a driven object varies with the frequency of the driver?

A
53
Q

What affect would increasing the amount of damping applied have on an oscillation?

A

It would reduce the amiplitude of the driven oscillation. It will also slightly reduce the frequncy that corresponds to the maxiumum amplitude of oscillation.

54
Q

What does the graph showing the effect of daming on the resonant responce of an oscillator look like?

A
55
Q

What are some examples of practicle applications of resonance?

A
  • Turning circuits that respond to a particular radio or TV frequency.
  • Microwave ovens cooking food due to the resonance of water molecules at a particular frequency.
  • The accurate timing mechanism of clocks and watches controlled by the resonant vibrations of quartz crystals.
56
Q

What are some problems of resonance?

A
  • In practise, most structures have several natural frequencies od oscillation, meaning bridges and tall buildings vibrate due to forcung by wind, earthquakes or traffic.
  • In poorly designed loudspeaker one or more frequencies produced from the electrical signal will be particularly loud, as the speakers parts are resonating at their natural frequencies.

module 5- newtonian world and astrophysics (5 decks)

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