Module 5 Simple Harmonic Motion

Question 1

Where is velocity at a maximum?

Answer 1

at the mean position when x = 0

Question 2

Where is velocity zero?

Answer 2

at the amplitude when x = +A or -A

Question 3

Explain why at the amplitude, velocity is zero?

Answer 3

mass is changing direction, velocity zero for an instant

Question 4

What is the definition for amplitude considering SHM?

Answer 4

the maximum displacement from the equilibrium/mean position

Question 5

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?

Answer 5

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

Question 6

Define simple harmonic oscillation?

Answer 6

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

Question 7

What is the symbol for angular displacement?

Answer 7

omega ω

Question 8

What are the units for ω?

Answer 8

rad*s^-1

Question 9

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

Answer 9

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

Question 10

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

Answer 10

Calculation in radians

ωt=ωT and ω=2π/T

So ωT=2π

cos(2π) = 1

1xA = A

Question 11

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

Answer 11

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

Question 12

Describe how to plot a graph of acceleration against displacement

Answer 12

Straight line through the origin

Negative gradient

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

Question 13

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

Answer 13

undamped

Question 14

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

Answer 14

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

Question 15

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

Answer 15

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)

Question 16

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

Answer 16

Kinetic energy

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

Question 17

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

Answer 17

Gravitational potential energy

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

Question 18

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

Answer 18

Elastic potential energy

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

Question 19

What is damping?

Answer 19

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

Question 20

What are the effects of damping?

Answer 20

Amplitude decreases

All types of energy (KE and PE) decrease

Maximum velocity decreases

Time period and frequency stay the SAME

Question 21

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

Answer 21

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

Question 22

What is used to measure whether something is decaying exponentially?

Answer 22

constant ratio property will be true at equal intervals

Question 23

What is the constant ratio property?

Answer 23

ratio of current to previous amplitude after each complete oscillation

Question 24

When will the natural frequency be observed?

Answer 24

when there are no external driving forces

Question 25

When will a system oscillate at the driving frequency?

Answer 25

when there is an external driving force

Question 26

Define resonance

Answer 26

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

Question 27

Describe the shape of a graph of amplitude to driving frequency

Answer 27

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

Question 28

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

Answer 28

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

Question 29

Use resonance to explain how microwave ovens work

Answer 29

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

Question 30

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

Answer 30

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

Question 31

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

Answer 31

periodic driving force

Question 32

In SHM, displacement is…

Answer 32

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

Question 33

The time period of an oscillation is…

Answer 33

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

Question 34

The frequency of an oscillation is…

Answer 34

the number of oscillations per unit time at any point.

Question 35

The angular frequency of an oscillation is…

Answer 35

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

Question 36

The phase difference is….

Answer 36

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

Question 37

Forced oscillations…

Answer 37

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

Question 38

Free oscillations occur when…

Answer 38

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