Chapter 17 Oscillations Flashcards

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1
Q

What is oscillations?

A

This is the number of cycles

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2
Q

What is the equilibrium position?

A

This is the starting position for an object that oscillates. In this position, the object will not move

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3
Q

What is displacement?

A

This is the distance in a specific direction away from the equilibrium position

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4
Q

What is amplitude?

A

This is the maximum displacement

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5
Q

Why displacement and not distance?

A

Because displacement has a direction

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6
Q

What is a period?

A

This is the time taken to complete one full oscillation

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7
Q

What is frequency?

A

This is the number of oscillations per second

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8
Q

What is phase difference?

A

The difference in the displacements of an oscillating object between two times

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9
Q

What is the symbol for phase difference? What is the unit?

A

Symbol:ø
Units: rad (radians)

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10
Q

What is angular frequency?

A

The motion of oscillating objects are related to angular velocity.
As an object oscillates its phase is measured using radians. Angular velocity and frequency can be related with the equation:
ω = 2πf
So the angular frequency of the oscillating object can be calculated.

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11
Q

What is simple harmonic motion?

A
This is a common type of oscillating motion where the acceleration of the object is given by the equation:
a = ω^2x
a = acceleration
ω^2  = a constant for the object
ω = the angular frequency for the object
x = the displacement of the object
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12
Q

What are 2 key features of simple harmonic motion?

A
  • the acceleration of the object is proportional to the displacement
  • The acceleration acts in the opposite direction to the displacement
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13
Q

For an object doing simple harmonic motion, what can be graphed? What does the graph look like?

A

Acceleration against displacement

It looks like a straight line

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14
Q

What is the gradient of a graph of acceleration?

A

It is -ω^2

ω = angular frequency for the object

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15
Q

What happens to the period of an oscillating object as the amplitude is increased? Why?

A

The period does not change

As the amplitude increases so does the average speed.

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16
Q

What is an oscillator called that has a period that does not change with amplitude?

A

It is an isochronous oscillator

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17
Q

What does the graph of displacement against time look like for an oscillating object with simple harmonic motion?

A

sinusoidal

18
Q

What does the graph of velocity against time look like for an oscillating object with simple harmonic motion?

A

sinusoidal

19
Q

What does the graph of acceleration against time look like for an oscillating object with simple harmonic motion?

A

sinusoidal

20
Q

What are the equations for displacement against time? When do you use them?

A
x = ACosωt
x = ASinωt

Sine is used when the object starts in the equilibrium position at T=0.
Cosine is used when the object starts at maximum amplitude at T=0.

21
Q

What is the equation for the velocity of an oscillating object?

A

V = ±ω√A^2 - x^2

22
Q

What is the equation for the maximum velocity of an oscillating object?

A

Vmax = ωA

23
Q

What happens to the total energy of a pendulum as it swings?

A

The total energy stays constant

24
Q

What happens to the kinetic energy of a pendulum as it swings?

A

At maximum displacement there is no kinetic energy

When it passes the equilibrium position, the kinetic energy is maximum

25
Q

What happens to the potential energy of a pendulum as it swings?

A

A maximum displacement there is the maximum potential energy and as it passes the equilibrium position there is no potential energy

26
Q

How does the total energy of a pendulum stay constant as it oscillates when the kinetic and potential energies constantly change? What are the assumptions?

A

At max displacement, all the energy is stored as potential energy and as the pendulum falls this potential energy is transferred into kinetic energy. As the pendulum rises the kinetic energy is transferred to potential energy.
This is assuming there are no resistive forces.

27
Q

What other oscillation shows a similar transfer of energy between kinetic and potential energy?

A

A spring with a weight attatched

28
Q

A glider is placed on an air bed and is connected with a spring. It oscillates from side to side, Energy is transferred from kinetic to elastic potential energy. What are the equations for this movement?

A
Ep = 1/2kx^2
Epmax = 1/2kA^2

Ek = 1/2kA^2 - 1/2kx^2 = 1/2k(A^2 - x^2)

29
Q

What is dampening?

A

It is the absorption of the energy of an oscillating object. This reduces its displacement and kinetic and potential energy

30
Q

What is light dampening?

A

This is when the amplitude changes gradually with time but the period of the oscillations are almost unchanged.

31
Q

What is heavy dampening?

A

This is when the amplitude changes dramatically with time and the period of the oscillation increases slightely

32
Q

What happens to the energy absorbed from dampening?

A

The energy is transferred into heat or other energy forms

33
Q

What is free oscillation?

A

This is the oscillation that occurs naturally when an object is released form its max amplitude position. It is not forced to oscillate.

34
Q

What is the frequency that an object oscillates at during free oscilation?

A

This is the natural frequency

35
Q

What is forced oscillation?

A

This is when a periodic driving force is applied to an oscillator forcing it to oscillate at the frequency of the driving force.

36
Q

What is the frequency of a driving force called?

A

The driving frequency

37
Q

How will an object resonate?

A

When the driving frequency is equal to the natural frequency

38
Q

What will happen to the amplitude when the driving frequency is equal to the natural frequency?

A

The amplitude will increase dramatically

39
Q

What are some examples of resonance?

A

Many pendulum clocks use it
Many musical instruments
Car radios
MRI Scans

40
Q

What happens as the amount of dampening increases? (3 things)

A
  • The amplitude of vibration at any frequency decreases
  • The maximum amplitude occurs at a lower frequency than the natural frequency. The lower it is when the dampening is increased
  • There is not as dramatic an increase in amplitude up to the maximum amplitude. The line on a graph of amplitude against driving frequency is flatter