Oscillations Flashcards

1
Q

Define displacement of wave

A

The distance of a point on a wave from its undisturbed position

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2
Q

Define amplitude

A

The maximum displacement from its undisturbed position

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3
Q

Define time period

A

The time taken for one complete oscillation

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4
Q

Define frequency

A

The number of vibrations per second of any oscillating system

f = 1/T

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5
Q

Define angular velocity, and state the equation to calculate it

A

Angular velocity is the rate of change of angle for a circulating object

ω = dθ/dt

ω = 2π/T
or ω = 2πf

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6
Q

Define angular frequency, and state the equation to calculate it

A

Angular frequency is the number of cycles per unit time

It uses the same equations as angular velocity

ω = 2π/T
or ω = 2πf

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7
Q

What is phase difference and what is it measured in?

A

Phase difference is how out of step two identical waves are. It is measured in degrees or radians.

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8
Q

How do you calculate phase difference?

A

t/T x 360 = degrees
or
t/T x 2π = rad

Where t is the time interval between two corresponding points on the waves, and T is the time period

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9
Q

State the conditions for a particle to perform simple harmonic motion

A
  • the acceleration of a particle is directly proportional to its displacement
  • the acceleration of the particle is directed in the opposite direction to the displacement
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10
Q

What are the shapes of the displacement/time, velocity/time and acceleration/time graphs of a particle in SHM, starting from rest position

A
  • displacement/time graph is a sine wave
  • velocity/time graph is a cosine wave
  • acceleration/time graph is a sine wave reflected in the x-axis
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11
Q

What are the relationships between displacement, velocity and acceleration for a particle in SHM?

A
  • the velocity is a maximum when the acceleration is zero and the displacement is zero
  • the acceleration is a maximum when the displacement is at a maximum and the velocity is zero
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12
Q

State the formal relationship between acceleration and displacement for a particle in SHM

A

acceleration ∝ -displacement
a ∝ -x

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13
Q

What is the constant of proportionality added to the relationship, a ∝ -x, and what equation does it form?

A

Constant of proportionality = ω² or (2πf)²

a = -ω²x
or a = -(2πf)²x

This is the general equation for SHM

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14
Q

Write the equation and it’s variations that can be used to calculate displacement, x, when x = 0 at t = 0

A

x = Asinθ
x = Asin(ωt)
x = Asin(2πft)

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15
Q

Write the equation and it’s variations that can be used to calculate displacement, x, when x = A at t = 0

A

x = Acosθ
x = Acos(ωt)
x = Acos(2πft)

or x = Asin(2πft + φ)

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16
Q

What are the equations for velocity and acceleration given by differentiating x = Asin(2πft)

A

v = 2πfAcos(2πft)
or v = ωAcos(ωt)

a = -(2πft)²Asin(2πft)
or a = -ω²t²Asin(ωt)

17
Q

State the equation for velocity containing amplitude and displacement, and hence state the equation for maximum velocity

A

v = +/- ω√(A² - x²)

Velocity is a maximum when displacement is zero

Therefore v max = +/- ωA
or v max = +/- 2πfA

18
Q

State what will happen to the period of a simple harmonic oscillator if its amplitude is changed

A

The period of a simple harmonic oscillator is independent of its amplitude. This means that the period stays the same when the amplitude is changed.

19
Q

What are the energy changes in SHM?

A

In an oscillation there is a constant interchange of energy between potential and kinetic, and if the system is undamped its total energy is constant

20
Q

What are the relationships between displacement, kinetic energy and potential energy for a system in SHM?

A
  • the kinetic energy is a maximum when the displacement is zero and potential energy is zero
  • the potential energy is a maximum when the displacement is at a maximum and the kinetic energy is zero
21
Q

State the equation for potential energy in a spring system

A

Ep = 1/2kx²

22
Q

State the equation for total energy

A

E total = 1/2kA²

23
Q

State the equation for kinetic energy, using the equations for E total and Ep

A

Ek = E total - Ep
Ek = 1/2kA² - 1/2kx²
Ek = 1/2k(A² - x²)

24
Q

Define the total potential energy of a system for a spring oscillating vertically

A

For a spring oscillating vertically, the total potential energy will be the sum of the elastic and gravitational potential energy of the system

25
State and describe the three types of damped motion
Under-damped motion - there is an exponential envelope Critical damping - no oscillation occurs, but the motion ceases in as short a time as possible Over-damped motion - no oscillation occurs but the time to return to the equilibrium position is longer than for the critical case
26
Define critical damping
Critical damping occurs when the motion ceases after the shortest possible time
27
What is a feature of an exponential envelope?
In equal times the amplitude is seen to fall by equal fractions Eg. if A1 A2 A3 etc are amplitudes after equal intervals of time then A1/A2 = A2/A3 etc
28
What is the difference between natural frequency and forcing frequency?
All systems have a natural frequency of oscillation, which could be SHM, a more complex harmonic motion or damped harmonic motion. An outside agent can apply a forcing frequency of any value, f, to the system. This forcing frequency is a source of energy, passed on to the system.
29
Define resonant frequency
When the forcing frequency is equal to the natural frequency of the system, then resonance is said to occur, and amplitude is a maximum
30
State the relationships between resonance and damping
- as we increase damping, the amplitude of the resonant vibration decreases - the resonant peak also becomes broader, and resonance occurs at a lower frequency