Resonance and Damping

Question 1

what two types of oscillations are there

Answer 1

free and forced oscillations

Question 2

when do free oscillations happen

Answer 2

• when a system performs oscillations

- free from the influence of any forces from outside the system

Question 3

what is a natural frequency

Answer 3

• the frequency any oscillating system naturally chooses to oscillate at
• when left alone to freely oscillate

Question 4

how could you change the free oscillation of the pendulum into a forced oscillation

Answer 4

• by externally exerting a force on the pendulum

- such as pushing the bob in the opposite direction its naturally oscillating to

Question 5

what is the name of the frequency you have now forced the pendulum to oscillate at

Answer 5

• the driving frequency

- specifically your driving frequency

Question 6

what is resonance

Answer 6

• a phenomenon which describes very large amplitude oscillations that occur
• when a driving frequency matches the natural frequency of the system

Question 7

why does the amplitude of an oscillation become very large during resonance

Answer 7

• because the system is absorbing the extra energy from the driving frequency
• this added to its natural frequency leads the increase of its amplitude

Question 8

what is going on inside a washing machine that causes it to sometimes be loud or quiet

Answer 8

• when loud the motor would be spinning at the same natural frequency of one of the panels
• this resonance results in large amplitudes which therefore results in loud noises
• when quiet the motors rotation generates vibrations at other frequencies that dont match the natural frequency of any part of the machine

Question 9

what will a graph of vibrational amplitude against frequency show for the washing machine example

Answer 9

• the line will be very shallow (at 0 basically) and have a very low gradient for most of the frequencies
• then it will begin to steeply rise and peak quickly
• only to quickly fall back down to low levels but be slightly higher than before
• with some sort of turbulence following the line

Question 10

what is the peak of that graph telling you

Answer 10

• the frequency at which resonance occurs

- and therefore the natural frequency of the panel

Question 11

there is a mass on a spring connected to a vibration generator connected to a signal generator. the mass on the spring is above a motion sensor that is connected to a computer that datalogs the height of the mass. what is the equation for the time period of the oscillation of the mass on a spring

Answer 11

T = 2pi * root of (m / k)

Question 12

what do each of those variables mean

Answer 12

• T= time period per oscillation
• m = mass of mass on spring
• k = spring constant

Question 13

given that is the equation for time period, what is the equation for frequency and why

Answer 13

• f = (1 / 2pi) * root of (k / m)

- because T = 1 / f

Question 14

what is the specific name of this frequency

Answer 14

the resonant frequency

Question 15

what does measuring the amplitude of forced oscillations allow us to find and why

Answer 15

• the resonant (natural) frequency
• because the forced oscillations are created from the driving frequency of the vibration generator
• and this is in resonance with the natural frequency

Question 16

how would we rearrange this equation to work out the mass

Answer 16

• f^2 = (1 / 4pi^2) *( k / m)
• f^2 = k / 4pi^2 m
• m = k / 4pi^2 f^2

Question 17

therefore what is the equation for working out the spring constant

Answer 17

k = 4pi^2 f^2 m

Question 18

what are damped oscillations

Answer 18

• oscillations which suffer a loss in energy each time they oscillate
• reducing their amplitude each time

Question 19

if a system is performing simple harmonic motion at its natural frequency, what two things could practically cause the dissipation of energy in that system

Answer 19

• a frictional force acting on the system

- or the plastic deformation of a ductile material in the system

Question 20

what is damping

Answer 20

the material or system causing an energy loss each damped oscillation

Question 21

what is an example of damping in a swinging pendulum

Answer 21

air resistance

Question 22

despite the amplitude of oscillations decreasing overtime, what still remains constant throughout

Answer 22

the time period for each oscillation

Question 23

what does it mean if a system is critically damped

Answer 23

• damping occurs such that the oscillator returns to its equilibrium position in the quickest possible time
• without going past that equilibrium position

Question 24

what would critical damping look like on a displacement-time graph

Answer 24

• the line would start on the top of the displacement axis

- then gently plateau onto the time axis and rest on it

Question 25

what is overdamping

Answer 25

- when the system has been damped too much | - causing the oscillator to take a very long time to return to its equilibrium position

Question 26

where is overdamping practically used

Answer 26

in car suspension systems

Question 27

what would overdamping look like on a displacement-time graph

Answer 27

- the line would start at the top of the displacement axis - then gently begin to plateau similar to the critical damping line - but it would stake significantly longer for it to reach the time axis - on most graphs it doesnt even reach it, its just left there suspended in the air

Question 28

what would a normally damped (underdamped) line look like on a displacement-time graph

Answer 28

- the line would start at the equilibrium position and begin to oscillate normally - but with each full oscillation the peaks become smaller - until the line is just hugging the time axis with minuscule amplitudes

Question 29

what would an undamped line look like on a displacement-time graph

Answer 29

like any other normal oscillation, having constant amplitudes

Question 30

what is the goal for most engineers when creating a damping system for an object

Answer 30

to create a good medium between underdamping, critical damping and severe overdamping

Question 31

what is a main issue engineers come across when trying to achieve this

Answer 31

one object can have multiple natural frequencies

Question 32

what kind of damping would we want a shock absorption system to have and why

Answer 32

- critical damping - because we want to make sure the system returns to equilibrium without overshooting - thereby stopping the oscillations as quickly as possble

Question 33

how do opera singers break wine glasses with their voice

Answer 33

- they sing at a pitch that matches the natural frequency of the wine glass - this causes resonance to occur within the wine glass - the very large amplitudes caused by resonance rattle the structure of the glass so much that it breaks

Question 34

what two properties do climbing ropes need to have and why

Answer 34

- they need to be stretchy to avoid a sudden and painful stop to a fall - but they need to be stiff enough to bring the climber to a halt

Question 35

how is this balance created in a climbing rope

Answer 35

- the rope consists of several woven strands | - there is a ratio of stretchy strands to stiff strands which make the ideal balance between a stretchy and stiff rope