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A2 Physics > Simple Harmonic Motion > Flashcards

Simple Harmonic Motion Flashcards

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1
Q

What is simple harmonic motion?

A

The motion of an object whose acceleration is proportional to its distance from a fixed point with this acceleration always being directed towards that point.

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2
Q

How is the displacement from the point of equilibrium calculated?

A

x = Acosωt

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3
Q

How is velocity at a given time calculated?

A

v = -ωAsinωt

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4
Q

How is the acceleration towards the point of equilibrium calculated?

A

a = -ω^2Acosωt

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5
Q

How is velocity at a displacement calculated?

A

v = ±ω√(A^2-x^2)

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6
Q

How is maximum velocity calculated?

A

Vmax = ±ωA

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7
Q

When does the maximum velocity occur?

A

At the equilibrium position

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8
Q

When does the minimum velocity occur?

A

At the maximum displacement

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9
Q

How is maximum acceleration calculated?

A

a_max = -ω^2A

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10
Q

When does the maximum acceleration occur?

A

When x = A, at maximum displacement

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11
Q

When does the minimum acceleration occur?

A

At the equilibrium position

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12
Q

How is time period calculated?

A

T = 2π/ω

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13
Q

How is frequency calculated?

A

f = 1/T

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14
Q

What is ω equal to?

A

2πf

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15
Q

When is the minus sign in an equation ignored?

A

When asked for the magnitude

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16
Q

What does the gradient of a displacement vs time graph give?

A

Velocity

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17
Q

What does the gradient of a velocity vs time graph give?

A

Acceleration

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18
Q

What function does a displacement vs time graph show?

A

Cosine

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19
Q

What function does a velocity vs time graph show?

A

-Sine

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20
Q

What function does an acceleration vs time graph show?

A

-Cosine

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21
Q

What does an acceleration vs displacement graph show?

A

A straight line with a negative gradient

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22
Q

How is the resulting force of a pendulum calculated?

A

F = -mgsinθ

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23
Q

What is the acceleration of a pendulum?

A

a = -gsinθ

24
Q

How is the time period of a pendulum calculated?

A

T = 2π√(l/g)

25
Q

When does sinθ = θ?

A

When the angle is small and θ is in radians.

26
Q

How is the maximum velocity of a pendulum calculated?

A

Vmax = ±A√(g/l)

27
Q

How is the maximum acceleration of a pendulum calculated?

A

a_max = -(g/l)A

28
Q

How is the velocity of a pendulum calculated?

A

v = ±(√[g/l])(√[A^2-x^2])

29
Q

What is the restoring force of a spring?

A

-kx provided Hooke’s Law applies

30
Q

How is the acceleration of an oscillating spring calculated?

A

a = -(k/m)x

31
Q

How is the time period of an oscillating spring calculated?

A

T = 2π√(m/k)

32
Q

How can the spring constant of an oscillating spring be found?

A

k = 4π^2 / gradient

33
Q

How is the frequency of an oscillating spring calculated?

A

f = (1/2π)(√[k/m])

34
Q

How is the maximum velocity of an oscillating spring calculated?

A

Vmax = ±(√[k/m])A

35
Q

How is the total energy of an oscillating system calculated?

A

0.5(mω^2)A^2 or 2mπ^2f^2A^2

36
Q

How can k be calculated in a system with two springs?

A

k = F/x

37
Q

How can the total energy in an oscillating spring system be calculated?

A

0.5kA^2

38
Q

What is an undamped system?

A

An SHM system in which no energy is lost.

39
Q

How does the amplitude of an undampened system change?

A

The amplitude is constant.

40
Q

What is a damped system?

A

An SHM system in which energy is lost to the surroundings

41
Q

How does the amplitude of a damped system change?

A

The amplitude decreases with time.

42
Q

What is a lightly damped system?

A

A system in which it takes many oscillation cycles before the amplitude falls to zero.

43
Q

What is a heavily damped system?

A

A system in which it the oscillations decay to zero after a few oscillations?

44
Q

What is an over damped system?

A

A system which will not oscillate.

45
Q

What is a critically damped system?

A

A system which will return to the equilibrium position in less than a quarter of the periodic time.

46
Q

What are free oscillations?

A

SHM with a constant amplitude and time period where there is no energy transfer.

47
Q

What are damped oscillations?

A

SHM in which the amplitude decreases due to damping forces in which energy is transferred to the surroundings.

48
Q

What are forced oscillations?

A

SHM that is driven by an external influence.

49
Q

What is resonance?

A

When one oscillating system is coupled to and producing forced oscillations in a second oscillating system.

50
Q

What is the natural frequency of a system?

A

The frequency at which a system oscillates when not subjected to a continuous or repeated external force.

51
Q

When is a responder resonating?

A

When the frequency of the driver matches the natural frequency of the responder.

52
Q

What is the phase difference between a responder and driver when there is resonance?

A

π/2

53
Q

What is the phase difference between a responder and driver when the driver is below the responder’s natural frequency?

A

~0

54
Q

What is the phase difference between a responder and driver when the driver is above the responder’s natural frequency?

A

~π

55
Q

How can the effects of resonance be decreased?

A

Damping

56
Q

Describe how simple harmonic motion in a spring can be shown experimentally.

A
  • Assemble a clamp and stand on a workbench.
  • Attach a spring with an IR position sensor alongside a metre rule.
  • Add masses to the spring then pull the assembly down a set amount giving the initial amplitude.
  • The masses will now oscillate in SHM as will be shown by the output of the position sensor.
57
Q

How does damping affect resonance?

A
  • Lightly damped systems will have a sharp resonance peak.

- Heavily damped systems are less sensitive to the driving frequency.

A2 Physics (9 decks)

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