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A Level Physics Paper 1 > Simple Harmonic Motion > Flashcards

Simple Harmonic Motion Flashcards

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1
Q

Examples of simple harmonic motion

A

Pendulum swinging
Mass bouncing on a spring
Particle in a solid vibrating backwards and forwards
Steel ball rolling in a curved dish

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2
Q

Two conditions for simple harmonic motion/definition

A

Acceleration of the object is always directed towards the equilibrium position
Acceleration is always proportional to the displacement of the object from the equilibrium position

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3
Q

How is acceleration related to displacement

A

a ∝ -x

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4
Q

How is time period related to amplitude

A

It isn’t
They are independant
Changing the amplitude will not affect the time period of oscillations

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5
Q

Three types of oscillations

A

Free
Damped
Forced

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6
Q

What is a free oscillation

A

An oscillation in which there are no external forces acting on the oscillating system

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7
Q

Equilibrium position

A

Position the object will always return to after oscillations have ceased

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8
Q

Displacement

A

Distance between the object and the equilibrium position

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9
Q

When is acceleration maximum

A

When displacement is maximum

a ∝ -x

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10
Q

When is acceleration minimum (zero)

A

When displacement is zero

a ∝ -x

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11
Q

When is velocity maximum

A

When displacement is zero

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12
Q

When is velocity minimum (zero)

A

When displacement is maximum

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13
Q

When is kinetic energy minimum

A

Maximum acceleration/maximum displacement

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14
Q

Total energy

A

Constant

Et=Ek+Ep

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15
Q

When is kinetic energy maximum

A

Minimum acceleration/displacement (zero)

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16
Q

When is potential energy minimum

A

Acceleration is zero/displacement is zero

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17
Q

When is potential energy maximum

A

Acceleration is maximum/displacement is maximum

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18
Q

Graph for total energy against time

A

Straight horizontal line that is positive

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19
Q

Displacement to velocity to acceleration

A

Differentiate

Differentiate graph using trig

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20
Q

Acceleration to velocity to displacement

A

Integrate

Integrate graph using trig

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21
Q

Phase relationship between displacement and velocity/velocity and acceleration

A

π/2

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22
Q

Phase relationship between displacement and acceleration

A

π

23
Q

When is x=Acos(wt) used

A

Displacement
Amplitude
Angular frequency x time to give angular displacement

If x=a when t=0

Must remember w is the angular frequency

24
Q

What can wt become

A

wt=2πft=2πt/T

t/T is how far through the cycle it is in radians

25
Q

Maximum kinetic energy

Hence, maximum potential energy and total energy

A

1/2 m w^2 A^2

Since m and w are constant
Ek ∝ A^2

26
Q

When is x=Asin(wt) used

A

Displacement
Amplitude
Angular frequency x time to give angular displacement

If x=0 when t=0

Must remember w is the angular frequency

27
Q

What factors affect the time period of a mass spring system

A

Mass

Spring constant

28
Q

What factors do not affect the time period of a mass spring system

A

Amplitude
Acceleration due to gravity
Shape of mass (air resistance)

29
Q

What factors affect the time period of a simple pendulum

A

Length of string

Acceleration due to gravity

30
Q

What must you bear in mind for simple pendulums simple harmonic motion

A

Only follow it at small amplitudes
A small swing is one in which the angle theta is small enough that sin theta can be approximated to theta when theta is measured in radians

31
Q

What is the angle of a simple pendulum is greater than 10 degrees

A

Wont undergo SHM

32
Q

How can you use a simple pendulum to find gravity

A

Set it up
Small angle of swing
Vary length of pendulum and record the time period
Repeat and mean
Plot Time period squared on y against length on x
Gravity is equal to 4π^2/gradient

33
Q

What is a damped oscillation

A

Oscillating systems energy decreases over time due to an external force acting on the system
Such as friction between two solid bodies
Viscous forces between solid body and a gas or liquid

34
Q

Consequence of a dampening force

A

Energy dissipated to surrounding
Amplitude decreases
Time period remains the same

35
Q

How is the damping force related to velocity

A

Damping force ∝ - Velocity^2

36
Q

When is the dampening force greatest

When is it smallest

A

Max at equilibrium where velocity is max

Minimum/zero at amplitude where velocity is zero

37
Q

Lightly damped system

A

Resisting force is small
Energy transferred to surroundings very slowly
System oscillated and the amplitude reduces gradually
Time period is the same

38
Q

Critical damping/critically damped system

A

Energy is transferred to surroundings very rapidly
Oscillator does not actually oscillate at all before coming to rest
A quarter of a cycle carried out

39
Q

Examples of critical damping

A

Car suspensions where you don’t want oscillations to occur

Moving coil analogue meters where you don’t want oscillations to occur

40
Q

Heavily damped system

A 
Dampening force is very large
System does not oscillate
Slowly returns to the equilibrium position
System has almost no kinetic energy
Only potential energy
41
Q

Natural frequency

A

f0

The frequency an object will oscillate at if there are no external forces acting on it

42
Q

Driving frequency

A

The frequency of oscillation when a system is being made to oscillate by a periodic external force

43
Q

Two parts to a forced oscillating system

A

Driver; the thing providing the external force and input energy
The driven; the part of the system receiving the input of energy and being made to oscillate

44
Q

Frequency of driver less than natural frequency

A

Low amplitude oscillations
Similar amplitude to driving force
In phase with the driving force

45
Q

Frequency of the driver is equal to natural frequency

A

Resonance occurs
Oscillations of amplitude increase
Much larger than the driving force
π/2 out of phase with the driving force

46
Q

Frequency of the driver is greater than the natural frequency

A

Low amplitude oscillations

π out of phase with driving force

47
Q

Resonance

A

Drivers frequency is equal to the natural frequency of the system being driven
Resulting in the system oscillating with a large amplitude

48
Q

Driving force the same direction as velocity

A

Work done on the system

Increases its energy

49
Q

Explain the graph for amplitude of driven system against frequency of driver for the types of damping

A

No damping asymptote at natural frequency and x axis
Light damping asymptote at x
Heavier damping asymptote at x

Heavier the damping the lower the peak amplitude and the smaller the area

Area decreases as damping increases/lines for each type of damping don’t overlap

All cross y intercept at same point and positive non zero

50
Q

Phase difference f

A

0

51
Q

Phase difference f=f0

A

90°

52
Q

Phase difference f>f0

A

180°

53
Q

Explain Bartons pendulum

A

Length the same as the driver pendulum: Same frequency so phase difference is 90° and resonance occurs

Length shorter than the driver: Larger frequency so phase difference is 0

Length longer than the driver: Smaller frequency so phase difference is 180°

A Level Physics Paper 1 (8 decks)

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