5.3 Oscillations Flashcards

1
Q

what is the definition of displacement (in terms of oscillations)?

A

displacement is the distance an object move from its equilibrium/rest position, may be positive or negative (in metres)

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2
Q

what is the definition of amplitude?

A

amplitude is the maximum displacement from the equilibrium position and will always be positive (in metre)

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3
Q

what is the definition of period?

A

period is the time taken for 1 complete pattern of oscillation at any point (in seconds)

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4
Q

what is the definition of frequency?

A

frequency is the number of oscillations per unit time at an point, number of cycles per second (in Hz)

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5
Q

what is the definition of phase difference?

A

phase difference,Φ, is the fraction of a complete cycle or oscillation between 2 oscillating points

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6
Q

what is the formula for angular frequency?

A

ω = 2π / T or ω = 2πf

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7
Q

what is the difference between angular velocity and angular frequency? which applies to circular motion and which applies to oscillations?

A

they have the same formula but angular frequency is the magnitude of the vector quantity of angular velocity, they are both measure in rad s^-1 but…
angular velocity –> circular motion (vector)
angular frequency –> oscillations (scalar)

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8
Q

what is the equation of simple harmonic motion?

A

a = -ω^2x
where a = acceleration
ω = angular frequency
x = displacement

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9
Q

what is simple harmonic motion?

A

when an object oscillates and the acceleration of the object is directly proportional to its displacement and acts in the OPPOSITE direction to he acceleration (towards the fixed midpoint)

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10
Q

what is the restoring force in oscillations (think of a pendulum)?

A

the restoring force acts in the opposite direction to the displacement (brings it back to the middle)

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11
Q

how do you determine the period/frequency of a simple harmonic oscillator?

A
  • to work out the frequency use 1 / T
  • the best place to time from is in the middle because there is less error than recording at maximum displacement because at max displacement the velocity is slower as its changing direction and spends more time there so timing at that point increases inaccuracy
  • you need to time for 10 oscillations then work out the mean and divide by 10
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12
Q

in SHM, are frequency and period dependent on the amplitude?

A

no, they DO NOT depend on the amplitude

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13
Q

what is an isochronous oscillator?

A

in SHM, the frequency and period are independent of the amplitude (they’re constant for a given oscillation) so a pendulum clock will keep ticking in regular time intervals even if its swing becomes very small, this kind of oscillator is called an isochronous oscillator

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14
Q

when is the velocity max in a swinging pendulum?

A

at the midpoint (where x = 0) most KE

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15
Q

when is the velocity 0 in a swinging pendulum?

A

when displacement is max (at the ends of the swing)

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16
Q

when is the displacement max in a swinging pendulum?

A

at the ends of the swing

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17
Q

when is the displacement 0 in a swinging pendulum?

A

at the midpoint, equilibrium position

18
Q

when is the acceleration max in a swinging pendulum?

A

when displacement is max (at the ends of the swing)

19
Q

when is the acceleration 0 in a swinging pendulum?

A

at the midpoint (where x = 0)

20
Q

what are the two ‘solutions’ to a = -ω^2x?

A

x = Asin(ωt) and x =Acos(ωt)

the angle must be in radians

21
Q

when should you use x = Asin(ωt)? (sine shape)

A

you should use it when you begin timing as the object passes through the midpoint where x = 0

22
Q

when should you use x =Acos(ωt)? (cos shape)

A

you should use it when you begin timing when the object is at its maximum displacement where x = max

23
Q

what is the equation for the velocity of a simple harmonic oscillator?

A
V = +- ω (A^2 - x)^0.5
where A = amplitude
ω = angular frequency
x = displacement from the rest point
the +- is present because velocity is a vector and could be in the positive or negative direction
24
Q

what is the equation for the MAX velocity of a simple harmonic oscillator? and how can you get to it from V = +- ω (A^2 - x)^0.5?

A

Vmax = +- ωA
(you can get it from making displacement (x) = 0 at max velocity using V = +- ω (A^2 - x)^0.5 which simplifies to the above equation)

25
Q

what is the equation for MAX acceleration?

A

Amax = ω^2A
where ω = angular frequency
A = amplitude
(LEARN THIS ONE)

26
Q

what does the gradient of a displacement time graph of a simple harmonic oscillator give you?

A

velocity

27
Q

what does the gradient of a velocity time graph of a simple harmonic oscillator give you?

A

acceleration

28
Q

in a swinging pendulum where is there max kinetic energy and max gravitational potential energy?

A

max kinetic energy = equilibrium/rest position

max gravitational potential energy = max displacement

29
Q

what is the mechanical energy?

A

the sum of the potential and kinetic energy is called the mechanical energy and stays constant (as long as the motion isn’t damped)

30
Q

what are the energy transfers in a vertical spring-mass system? at max displacement, equilibrium postion and at max displacement?

A

at max displacement, (when stretched fully)
KE = 0
GPE = Min
EPE = Max

equilibrium position
KE = Max
GPE = 0.5xMax
EPE = In between

at max displacement, (at the top)
KE = 0
GPE = Max
EPE = Min

31
Q

what frequency will free oscillators vibrate at?

A

their natural frequency

32
Q

what is a free oscillator?

A

an oscillator that is set into motion and has no periodic driving force acting on it, then it is described as a free oscillator

33
Q

what are forced vibrations?

A

when there is an external driving force, the frequency of this force is called the driving frequency

34
Q

what is resonance?

A

when the driving frequency is equal to the natural frequency, body will oscillate with max amplitude and at natural frequency

35
Q

what does the amplitude-frequency graph look like for natural frequency?

A

high sharp peak somewhere in the middle

36
Q

what can Barton’s pendulums highlight? (page 69)

A

demonstration of resonance, the ball with the same length of string as the driver pendulum will perform oscillations with the greatest amplitude

37
Q

what is damping?

A

damping forces reduce the amplitude of an oscillation with time, due to energy being removed from the oscillating system

38
Q

what are some real life applications of damping?

A

car shock absorbers (suspension systems of cars) to make the ride as comfortable as possible

39
Q

what is very heavy damping sometimes referred to as (can make oscillations die away)?

A

critical damping

40
Q

what are some examples of free oscillators?

A
  • a pendulum swinging
  • a mass-spring system
  • a fishing float bobbing on the surface of water
41
Q

what are some examples of forced oscillators?

A
  • a child being continually pushed on a swing
  • a building vibrating during an earthquake
  • the beating of a hummingbird’s wings