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Xaverian Physics > Module 5 Simple Harmonic Motion > Flashcards

Module 5 Simple Harmonic Motion Flashcards

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1
Q

Where is velocity at a maximum?

A

at the mean position when x = 0

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2
Q

Where is velocity zero?

A

at the amplitude when x = +A or -A

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3
Q

Explain why at the amplitude, velocity is zero?

A

mass is changing direction, velocity zero for an instant

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4
Q

What is the definition for amplitude considering SHM?

A

the maximum displacement from the equilibrium/mean position

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5
Q

Explain how a graph of displacement against time and acceleration against time can be used to show that they are directly proportional but in opposite directions?

A

Comparison of the two graphs shows a phase difference of 180°

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6
Q

Define simple harmonic oscillation?

A

a type of oscillation where acceleration is directly proportional to displacement but in the opposite direction

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7
Q

What is the symbol for angular displacement?

A

omega ω

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8
Q

What are the units for ω?

A

rad*s^-1

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9
Q

When is the formula x=Asin(ωt) used over x=Acos(ωt) used?

A

When at t=0 the displacement is zero, use sin

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10
Q

Explain how when using x=Acos(ωt), if t=T where T is the time period, will the displacement be the amplitude

A

Calculation in radians

ωt=ωT and ω=2π/T

So ωT=2π

cos(2π) = 1

1xA = A

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11
Q

How you find the maximum velocity of an object in SMH?

A

Vmax=±ωA (originally (A^2-x^2) cancels out to A^2 as displacement x is zero at max velocity)

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12
Q

Describe how to plot a graph of acceleration against displacement

A

Straight line through the origin

Negative gradient

Need to show A, -A, amax and -amax on the axes

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13
Q

What is the word for a system undergoing SMH with no resistive forces at play?

A

undamped

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14
Q

For an undamped system, describe the changes in KE and PE as the mass moves from the centre to the amplitude

A

At x = 0, V = max therefore KE = max, PE = min

At x = A, V = 0 therefore KE = 0, PE = max Loss of KE = Gain in PE

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15
Q

Explain how the height of a pendulum moved can be calculated using energy equations

A

KE=1/2m(vmax^2) at x = 0

PE=mgh at x = A

Loss from max KE = gain in PE

1/2m(v_max)^2=mgh (mass cancels out)

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16
Q

Describe the changes in KE of a undamped spring system in SMH

A

Kinetic energy

Bottom - KE is zero
Bottom to middle - KE increases to max at x = 0
Middle to top - KE falls to zero

17
Q

Describe the changes in GPE of a undamped spring system in SMH

A

Gravitational potential energy

Bottom - GPE minimum
Bottom to middle - GPE increases
Middle to top - GPE increases to maximum

18
Q

Describe the changes in elastic potential energy of a undamped spring system in SMH

A

Elastic potential energy

Bottom - EPE maximum
Bottom to middle - EPE falls
Middle to top - EPE falls to minimum

19
Q

What is damping?

A

the removal of energy from a system in SMH
due to work done against resistive forces producing heat

20
Q

What are the effects of damping?

A

Amplitude decreases

All types of energy (KE and PE) decrease

Maximum velocity decreases

Time period and frequency stay the SAME

21
Q

For a damped system, describe the observed changes during one oscillation

A

Mass moves a shorter distance at a lower speed, but takes the same amount of time to complete the oscillation

22
Q

What is used to measure whether something is decaying exponentially?

A

constant ratio property will be true at equal intervals

23
Q

What is the constant ratio property?

A

ratio of current to previous amplitude after each complete oscillation

24
Q

When will the natural frequency be observed?

A

when there are no external driving forces

25
Q

When will a system oscillate at the driving frequency?

A

when there is an external driving force

26
Q

Define resonance

A

if the driving frequency (f_d) is equal to the natural frequency (f_0) then resonance occurs where there is maximum energy transfer and the system oscillates with maximum amplitude

27
Q

Describe the shape of a graph of amplitude to driving frequency

A

flat line with a narrow peak at a given driving frequency ( when it equals the natural frequency)

28
Q

How will the shape of a graph of amplitude to driving frequency compare for a damped system?

A

same shape but lower amplitude for all frequencies (peak moves to the left slightly )

29
Q

Use resonance to explain how microwave ovens work

A

Microwave produces a driving frequency = the natural frequency of water molecule vibrations

Resonance occurs and thus water molecules move with maximum amplitude and heat the food by transferring energy

30
Q

Use resonance to explain why a tall building falls during an earthquake

A

A tall building oscillates with a natural frequency which is equal to the earthquake waves driving frequency

Resonance occurs and the building oscillates with maximum amplitude and thus collapses

31
Q

How must you refer to a driving force in terms of applying it to observe resonance?

A

periodic driving force

32
Q

In SHM, displacement is…

A

the distance moved by an object from its mean (or rest) position.

33
Q

The time period of an oscillation is…

A

the time for one complete oscillation to take place at any point.

34
Q

The frequency of an oscillation is…

A

the number of oscillations per unit time at any point.

35
Q

The angular frequency of an oscillation is…

A

2π multiplied by the frequency and describes the angle moved in radians per unit time.

36
Q

The phase difference is….

A

..the angle in radians between two oscillations. If the oscillations are in phase, the phase difference is 0 or a multiple of 2 π.

37
Q

Forced oscillations…

A

…occur when a driving force acts on the object in order to keep it oscillating.

38
Q

Free oscillations occur when…

A

…an object oscillates without a driving force . Objects undergoing free oscillations vibrate at their natural frequency.

Xaverian Physics (26 decks)

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