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Physics > Simple Harmonic Motion (Need to add RP) > Flashcards

Simple Harmonic Motion (Need to add RP) Flashcards

1
Q

What is simple harmonic motion

A

A specific type of oscillation where there is repetitive movement back and forth through an equilibrium position.

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2
Q

What is the time period for each complete vibration in SHM

A

Time interval is the same

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3
Q

In which direction does the restoring force act

A

Always directed horizontally or vertically towards the equilibrium position

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4
Q

Relationship between distance from equilibrium and the restoring force

A

Directly proportional

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5
Q

Examples of SHM

A

Pendulum of a clock
Child on a swing
Mass on a string

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6
Q

Condition for SHM

A

The acceleration is proportional to the horizontal or vertical displacement
The acceleration is in the opposite direction to the displacement

a is directly proportional to -x

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7
Q

Acceleration of an object oscillating in SHM =

A

-angular velocity^2 x displacement

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8
Q

State the velocity, acceleration and force when the displacement = +max

A

Velocity = 0
Acceleration = -max
Force = -max

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9
Q

State the velocity, acceleration and force when the displacement = -max

A

Velocity = 0
Acceleration = +max
Force = +max

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10
Q

State the velocity, acceleration and force when the displacement = 0

A

Velocity = max
Acceleration = 0
Force = 0

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11
Q

What does the graph of acceleration against displacement look like

A

Straight line through the origin sloping downwards (like y = -x)

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12
Q

Velocity in terms of displacement

A

Rate of change of displacement

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13
Q

Acceleration in terms of velocity

A

Rate of change of velocity

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14
Q

What does a displacement-time graph look like, when oscillation start from equilibrium

A

Sine curve

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15
Q

What does velocity-time graph look like, when oscillation start from equilibrium

A

Cosine curve

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16
Q

What does acceleration-time graph look like, when oscillation start from equilibrium

A

negative sine curve

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17
Q

How are all the graphs derived

A

v-t graph derived from gradient of x-t graph
a-t graph derived from gradient of v-t graph

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18
Q

Equation for restoring force

A

Force = -kx

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19
Q

What happens to the time period of the oscillation as spring constant increases

A

The spring will be stiffer and the time period of the oscillation will be shorter

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20
Q

What does the time period of a pendulum depend on

A

Gravitational field strength, therefore would be different on different planets

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21
Q

sin theta in a pendulum =

A

approximately theta as the formula is limited to small angles (smaller than 10 degrees)

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22
Q

What is the restoring force of the pendulum

A

The weight component acting along the arc of the circle towards the equilibrium position and is resolved to act act at and angle theta to the horizontal x.

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23
Q

Why is it assumed the restoring force in SHM in a pendulum acts along the horizontal

A

Because of small angle approximation

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24
Q

Which equation do you use for situations such as liquid in a U-tube

A

The same as the equation for a simple pendulum as it can be modelled in the same way

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25
Q

What energies are involved in the swinging of a pnedulum

A

GPE and KE

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26
Q

What energies are involved in the horizontal oscillation of a mass on a spring

A

Elastic potential and Kinetic energy

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27
Q

In a mass-spring system where is the max elastic potential energy

A

When the spring is stretched beyond its equilibrium position

28
Q

What happens to KE when the mass in a mass-spring system is released

A

Mass moves back towards equilibrium position and it accelerates and causes KE to increase

29
Q

When is KE at its max in a mass-spring system

A

At equilbrium position

30
Q

When is EPE at its minimum in a spring system

A

At equilibrium position

31
Q

What happens to KE and EPE once past the equilibrium position in a mass spring-system

A

KE decreases and EPE increases

32
Q

When is the GPE max in a simple pendulum

A

At the amplitude top of the swing

33
Q

What happens to KE when the pendulum is released

A

Pendulum moves back towards the equilibrium position and accelerates so the KE increases

34
Q

What happens to the GPE as the height of the pendulum decreases

A

GPE decreases

35
Q

What happens to both GPE and KE once the mass has passed the equilibrium position

A

KE decreases and GPE increases

36
Q

What happens to the total energy of a simple harmonic system

A

It always remains constant and is equal to the sum of KE and GPE/EPE

37
Q

Key features of an energy-displacement graph

A

Potential energy is at max at the amplitude and 0 at the equilibrium and is represented by U shape
KE is 0 at amplitude and max at the equilibrium position and is represented by an n shape
Total energy is represented by a horizontal straight line

38
Q

Key features of an energy-time graph

A

KE and potential energy are always in complete opposite positions. e.g. max KE = min PE

39
Q

What is damping (simple)

A

A resistive force that causes an oscillating object to stop oscillating such as friction and air resistance

40
Q

What are the 3 types of damping

A

Light damping
Heavy damping
Critical damping

41
Q

What direction does damping force act in

A

Opposite to velocity
It is proportional to negative velocity

42
Q

Damping (definition)

A

The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system

43
Q

How long does a damping force last

A

Until the oscillator comes to rest at the equilibrium position

44
Q

What happens to the frequency of damped oscillations as the amplitude decreases

A

The frequency DOES NOT CHANGE as the amplitude decreases

45
Q

Light damping characteristics

A

The amplitude does not decrease linearly, but exponentially with time
Lightly damped oscillating will oscillate with gradually decreasing amplitude
Time period is the same

46
Q

Features of a displacement-time graph for a lightly damped system

A

Many oscillations represented by a sine or cosine curve with gradually decreasing amplitude over time
Height of curve decreasing in both positive and negative displacement values
Amplitude decreases exponentially
Time period is the same and peaks and troughs are equally apart

47
Q

Critical damping characteristics

A

A critically damped oscillator returns to rest at its equilibrium position in shortest time possible without oscillating

48
Q

Features of a displacement-time graph for a critically damped system

A

System does not oscillate so displacement falls to 0 straight away
Fast decreasing gradient until it reaches the x axis
When oscillator reach equilibrium, the graph is a horizontal line at x=0 for remaining time

49
Q

Heavy damping characteristics

A

Takes a long time to return to equilibrium position without oscillating
System returns to equilibrium more slowly than critical damping

50
Q

Key features of a displacement-time graph for heavily damped system

A

No oscillations so displacement does not pass zero
Slow decreasing gradient until it reaches x axis
Once oscillator reaches equilibrium position, the graph remains a horizontal line

51
Q

Difference between resistive force and restoring force

A

Resistive force opposes the motion/velocity of the oscillator and causes damping
Restoring force is what brings the oscillator back to equilibrium position

52
Q

When do free oscillations occur

A

When there is no transfer of energy to or from the surroundings.
This happens when an oscillating system is displaced and left to oscillate

53
Q

Free oscillation

A

An oscillation when there are only internal forces and no external forces acting and there is no energy input

54
Q

Forced oscillations

A

Oscillations acted on by a periodic external force where energy is given in order to sustain oscillations

55
Q

Why must a periodic force be needed to sustain oscillations in a SHS

A

To replace the energy lost in damping. The periodic force does work on the resistive force decreasing the oscillations.

56
Q

What frequency does a free vibration oscillate at

A

Its resonant frequency

57
Q

What frequency do forced oscillations vibrate at

A

The same frequency as the oscillator creating the external, periodic driving force

58
Q

Natural frequency (f0)

A

The frequency of an oscillation when the oscillating system is allowed to oscillate freely

59
Q

Resonance

A

When the frequency of the applied force to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly

60
Q

Why is amplitude greatest at resonance

A

Energy is transferred from the drive to the oscillating system most efficiently therefore the system transfers the max KE possible

61
Q

Features of a driving frequency against amplitude graph / resonance curve

A

When f < f0 , the amplitude increases (f is the driving frequency, f0 is natural frequency)
At the peak where f = f0 , the amplitude is at its max - resonance
when f > f0, the amplitude starts to decreases

62
Q

Effect of damping on resonance

A

Damping reduces the amplitude of resonance vibrations
Height and shape of curve changes on the degree of damping

63
Q

Effect of damping on the natural frequency

A

It remains the same

64
Q

What happens to resonance graph as the degree of damping increases

A

Amplitude of resonance vibrations decrease - peak is lower
Resonance peak broadens
Resonance peak moves slightly to the left of the natural frequency when heavily damped

65
Q

Overall effect of damping on the resonance and amplitude

A

Reduces sharpness of resonance and reduces amplitude at resonant frequency

66
Q

What happens to resonant frequency at heavier damping

A

Resonant frequency becomes slightly less than f0

67
Q

Examples of where resonance occurs

A

An organ pipe
Glass smashing from a high pitched sound

Physics (10 decks)

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