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A Level Physics Paper 1 > Simple Harmonic Motion > Flashcards

Simple Harmonic Motion Flashcards

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

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
Maximum kinetic energy | Hence, maximum potential energy and total energy
1/2 m w^2 A^2 Since m and w are constant Ek ∝ A^2
26
When is x=Asin(wt) used
Displacement Amplitude Angular frequency x time to give angular displacement If x=0 when t=0 Must remember w is the angular frequency
27
What factors affect the time period of a mass spring system
Mass | Spring constant
28
What factors do not affect the time period of a mass spring system
Amplitude Acceleration due to gravity Shape of mass (air resistance)
29
What factors affect the time period of a simple pendulum
Length of string | Acceleration due to gravity
30
What must you bear in mind for simple pendulums simple harmonic motion
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
What is the angle of a simple pendulum is greater than 10 degrees
Wont undergo SHM
32
How can you use a simple pendulum to find gravity
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
What is a damped oscillation
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
Consequence of a dampening force
Energy dissipated to surrounding Amplitude decreases Time period remains the same
35
How is the damping force related to velocity
Damping force ∝ - Velocity^2
36
When is the dampening force greatest | When is it smallest
Max at equilibrium where velocity is max | Minimum/zero at amplitude where velocity is zero
37
Lightly damped system
Resisting force is small Energy transferred to surroundings very slowly System oscillated and the amplitude reduces gradually Time period is the same
38
Critical damping/critically damped system
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
Examples of critical damping
Car suspensions where you don't want oscillations to occur | Moving coil analogue meters where you don't want oscillations to occur
40
Heavily damped system
``` 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
Natural frequency
f0 The frequency an object will oscillate at if there are no external forces acting on it
42
Driving frequency
The frequency of oscillation when a system is being made to oscillate by a periodic external force
43
Two parts to a forced oscillating system
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
Frequency of driver less than natural frequency
Low amplitude oscillations Similar amplitude to driving force In phase with the driving force
45
Frequency of the driver is equal to natural frequency
Resonance occurs Oscillations of amplitude increase Much larger than the driving force π/2 out of phase with the driving force
46
Frequency of the driver is greater than the natural frequency
Low amplitude oscillations | π out of phase with driving force
47
Resonance
Drivers frequency is equal to the natural frequency of the system being driven Resulting in the system oscillating with a large amplitude
48
Driving force the same direction as velocity
Work done on the system | Increases its energy
49
Explain the graph for amplitude of driven system against frequency of driver for the types of damping
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
Phase difference f
0
51
Phase difference f=f0
90°
52
Phase difference f>f0
180°
53
Explain Bartons pendulum
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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