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Henry Physics RSFC > Circular Motion and SHM > Flashcards

Circular Motion and SHM Flashcards

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1
Q

What kind of motion will a pendulum perform?

A

Simple harmonic motion

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2
Q

If the graph of displacement is cos(x), what will the respective graphs of velocity and acceleration look like SHM?

A

Velocity as -sin(x)
Acceleration as -cos(x)

Same as SVA in maths for differentiating / integrating

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3
Q

Describe a freely oscillating object

A

It oscillates with a constant amplitude because there is no external force acting on it

(Its energy is constant)

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4
Q

What is natural frequency?

A

The frequency of free oscillations of an oscillating system.

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5
Q

What are forced vibrations?

A

Making an object oscillate at a frequency that is not it’s natural frequency

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6
Q

When does resonance occur?

A

When the frequency of driving force or oscillation matches the natural frequency of the system.

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7
Q

What is the outcome of resonance?

A

An increase in amplitude of the system’s oscillation.

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8
Q

What is damping?

A

The term used to describe the removal of energy from an oscillating system.

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9
Q

What are the three levels of damping?

A

Light
Heavy
Critical

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10
Q

Describe the motion of a lightly damped system

A

The system oscillates over a long time frame before coming to rest.
The amplitude of the oscillations exponentially decay. But the time period of oscillations remains constant

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11
Q

Describe heavy damping (over damping)

A

System not allowed to oscillate.

Slowly returns to equilibrium.

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12
Q

Describe critical damping

A

The oscillating system returns to the zero position of the oscillation after one quarter of a time period.

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13
Q

What are the two conditions for SHM?

A
  1. Acceleration must be proportional to displacement
  2. Acceleration must be opposite to displacement
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14
Q

Label up the maximum and minimum velocities and accelerations on the simple pendulum…

A
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15
Q

Label up the maximum and minimum velocities and accelerations on the mass spring system…

A
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16
Q

Label up the maximum and minimum potential and kinetic energies on the simple pendulum…

A
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17
Q

What are the kinetic energy, potential energy and total energy lines for one cycle of SHM?

A
18
Q

When do you use?

x=Acos(wt)

When do you use?

x=Asin(wt)

A

x=Acos(wt) -> displacement in SHM when x=A when t=0

x=Asin(wt) -> displacement in SHM when x=0 when t=0

MUST BE IN RADIANS

19
Q

How do you calculate KEmax or PEmax or ET in SHM?

A
20
Q

What two factors affect the time period of a mass spring system in SHM?

A
  1. Mass on the end of the spring
  2. Spring constant (stiffness) of spring
21
Q

What two factors affect the time period of a simple pendulum in SHM?

A
  1. Length between top of string and centre of bob
  2. Gravitational field strength
22
Q

What could the graph of energy against displacement look like in SHM?

A
23
Q

Does circular motion count as SHM?

A

When projected onto a flat surface, yes it does

24
Q

When a SHM system is lightly damped what happens to its amplitude and time period?

A

Amplitude decreases (as it loses energy)

But time period remains constant

25
Q

How is natural frequency determined for a mass spring system?

A
26
Q

How is natural frequency determined for a simple pendulum?

A
27
Q

What happens if the frequency of driving force is less than the natural frequency of a system?

f>f0

A

Low amplitude oscillations

Force and system oscillate with a constant phase difference of 0

28
Q

What happens if the frequency of driving force matches the natural frequency of a system?

f=f0

A

Resonance occurs

Large amplitude oscillations

Force and system oscillate with π/2 constant phase difference

29
Q

What happens if the frequency of driving force is more than the natural frequency of a system?

f>f0

A

Low amplitude oscillations

Force and the system oscillate with a constant phase difference of π

30
Q

The graph below shows driven oscillations with varying frequencies.

Add two lines if the system is:

  1. Undamped (free oscillations)
  2. Over damped
A
31
Q

For Barton’s pendulum which two balls oscillate?

A

P and Y because they have the same length

So natural frequency of y matches frequency of driving force from P

Y resonates and its amplitude is the largest with a phase difference of π/2 compared to P

32
Q

How does the time period differ for two pendulums of different amplitudes?

A

Time period is the same for both pendulums.

Time period is independent of amplitude

33
Q

What are some examples of simple harmonic motion?

A
  • A pendulum
  • A mass bouncing on a spring
  • Modelling atomic bonds
34
Q

What does KEmax equal?

A

KEmax = PEmax = Total energy = ½mω2A2

35
Q

How do you calculate total energy at any point in SHM?

A

KE + PE at that point

36
Q

When do pendulums undergo SHM?

A

When θ is small (less than 10 degrees / 1/18π radians)

37
Q

Describe damping forces and their relation to velocity

A

Damping forces always oppose motion

Damping forces ∝ v2

Therefore, damping forces are max at x=0 and min at x=A

38
Q

What are forced oscillations?

A

Oscillations produced by an external periodic force that has its own associated frequency

39
Q

What will happen if pendulum y on Barton’s pendulum is released, in reference to the shorter pendulum x?

X has a shorter length than y

A

Therefore, x has a larger natural frequency

X will oscillate with a smaller amplitude and phase difference of 0 radians

40
Q

What will happen if pendulum y on Barton’s pendulum is released, in reference to the longer pendulum z?

Z has a greater length than y

A

z has a smaller natural frequency than y

Z oscillates at a lower amplitude with phase difference π radians

41
Q

If the graph of displacement is sin(x), what will the respective graphs of velocity and acceleration look like for SHM?

A

Velocity is cos(x)

Acceleration is -sin(x)

Same as SVA in maths for differentiating / integrating

42
Q

What angle unit must you use for SHM?

A

Radians

Henry Physics RSFC (27 decks)

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