Class Opener: Resonance and Natural Frequency, Uses and Precautions

• What do you know already about resonance?

• What are forced oscillations?

• What is natural frequency?

• What happens when forced oscillations (little pushes) match the natural frequency of an object?

• Where is resonance useful?

• How are oscillations ‘damped’ when they are not wanted?

Resonance and Natural Frequency, Uses and Precautions

Grade 11 PhysicsNIS, Taldykorgan

Complicated by Mr. MartyAnimated slides from Timothy K.

Lund and Andrew Fawcett

Objectives: Resonance and Natural Frequency, Uses and Precautions

1) “describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system, and understand qualitatively the factors that determine the frequency response and sharpness of the resonance”

2) “show an appreciation that there are somecircumstances in which resonance is useful and other circumstances in which resonance should be avoided”

In order to get as high as you can on a swing , you ‘kick out’ at precisely the right time and frequency.

When you must match the natural frequency of the swing, your swinging arch and amplitude will grow.

The natural frequency depends on the length of the swing.

The swing is undergoing forced oscillations because you are applying a force as you kick.To increase the amplitude of SHM,

the forced oscillations must be in phase with andat the natural frequencyof the SHM you are driving.

Everyone Experience with Natural frequency of vibration and forced oscillations

What is meant by resonance?• If a system is forced to oscillate at its natural frequency

‘f0‘ , the amplitude of the motion will increase and we say that the system is in resonance.

• All objects have a natural frequency. For example a wine glass will ring at its natural frequency f0.

• If someone sings loudly enough at f0 ,the glass can be made to resonate and the amplitude may grow enough to shatter the glass.

The word resonance comes from Latin and means to

"resound" - to sound out together with a loud sound.

English Russian KazakhTo Resonate (verb)

Resonance (noun)

Natural Frequency ‘fo’

Forced Oscillation or Driving Vibration ‘f’

Amplitude

Damped vibrations

Observe the amplitude x0 as we adjust the red driving force’s frequency f:

describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system

Driving force at freq. f

Oscillating system at freq. f0

Driving force frequency ff0

Osc

illat

ing

syst

em a

mp

litu

de

x0

A

B

CA

B

C

f < f0

f = f0

f > f0

x0

x0

x0

Amplitude vs. Frequency plot near resonance

The

fre

qu

en

cy o

f th

e s

yste

mis

al

way

s f 0

Resonance from Teachable and Julie Rees.

• Every oscillating system has a “natural frequency”. This is the frequency at which it will oscillate freely.

• The natural frequency, fo, is affected by the dimensions and type of system. (A simple pendulum has a natural frequency which is dependent on the length of the pendulum only).

• If driven at this frequency, the oscillating system will achieve large amplitudes easily. When this happens, the system is said to be “resonating”.

@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

Producing Oscillations from Teachable and Julie Rees

• Pushing a swing is a simple example of using a “driving” force to produce oscillations.

• The frequency of the pushing force is the “driving frequency”. When this matches the natural frequency of the swing, the greatest amplitude will be reached by the child on the swing.

• If the driving frequency is higher or lower, the amplitude attained will not be as high as before.

Driving f

Amplitude

x

fo

x

x

reso

nance

Barton’s pendulums can be used to demonstrate this.

@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

Resonance; helpful or hindrance?

Helpful Hindrance

Some musical instruments

“Resonating guitars”

Vibrations of buildings during

earthquakes.

“Vibrating buildings”

Microwave cooking Vibrations of long bridges

(may be initiated by

moderate winds)

“Galloping Gertie”

Magnetic resonance

imaging (medical

diagnosis)

Vibrations of boxes

holding base speakers

A helpful site@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

Describe examples of resonance where it is useful, and where it is not.

EXAMPLE:The Sears Tower was designed to dampen the energy from the windy city’s wind so that the period of the top is in minutes, rather than seconds and its amplitude is small. Why?The Tacoma Narrows Bridge was not properly designed for dampening. On a windy day it began to resonate.

When the twisting motion was at the maximum, elevation of the

sidewalk at the right was 8.5m higher than the sidewalk at the left.

The deck was built on a 2 meter I-beam girder which split the airflow

causing vortices to form. These swirling air currents pushed the bridge into

a torsional or twisting motion. The frequency of this pushing matched

the natural resonant frequency of the deck leading to large amplitude motion and failure of the supporting I-beam leading to collapse.

The new Tacoma Narrows Bridge:How does the construction of the road deck differ

from that seen in the video clip?

YouTube links for Bridge Resonance• Why Physics Is Awesome: The Power Of

Resonance!https://www.youtube.com/watch?v=urYWaHfel6g

• Tacoma Narrows Bridge Collapse (no sound Good footage)

https://www.youtube.com/watch?v=lXyG68_caV4

• Millennium Bridge London:http://www.youtube.com/watch?v=gQK21572oSU&feature=PlayList&p=7C51D65943

955ACB&playnext_from=PL&playnext=1&index=36

• Collapse of the Tacoma Narrows Bridge on the 7th November, 1940 (compared to GGB)

https://www.youtube.com/watch?v=KVc7oBKzq9U

• Barton's Pendulum; A lab called “Ghostly Weights”https://www.youtube.com/watch?v=kODOL-QBzSM

LOMA PRIETA Earthquake: 17 October 1989 magnitude of 7.0, occurred on the San Andreas Fault

The Nimitz Freeway or ‘Cypress Street Viaduct’, California’s first double-decker freeway: before and after the earthquake.

The collapsed Nimitz Freeway from the air!

Famous bridges that did not show Resonance:

• Tulpar and Maral bridges over the Ishim River

• Golden Gate Bridge

• Verrazano Narrows Bridge

• Semipalatinsk Irtysh River Bridge

Describe examples of resonance where it is useful

EXAMPLE:When you tune in a radio receiver you are changing the resonant frequency of the circuitry so that one particular station comes in loud and clear.Which curve is best?

Tuner f

amp

litu

de

October 15, 2009 NJIT New Jersey Institute of Technology

Resonance for advanced students• The long term solution for the driven oscillator is

for t >> 1/b, where the amplitude, as we have seen, is

• This amplitude expression is interesting, because it says that as you drive a system at frequency w, its amplitude depends on both how far off you are from the resonant frequency wo, and also on how big the damping is.

• If there is no damping at all, and you drive the system at the resonant frequency, then both terms

• In this case, the amplitude goes to infinity. The way to think about this is that the driving force pumps energy into the oscillator (like pushing a child on a swing), and if there is no dissipation, there is no loss of energy and the energy grows to become infinite.

• If you tune the driver frequency (variable w) for a given oscillator (fixed wo), what is the value of w for which A2 is maximum?

,cos)( w tAtx

.

4 22222

o

2

o2

wbww

fA

.04 and 0 22222

o wbww

wo

w

A2 tuning aradio

2 2

2 o 2 .w w w b

The underlying implication of the above is that there is no friction force and no drag force. Then ET is constant.

Note that the amplitude of the is placement x remains constant, shown in A.

If there is friction or drag, ET

decreases over time as does the amplitude, shown in B and C.

We say that the oscillations have been damped.

Note that damping does not affect period T or frequency f.

State what is meant by damping

EK + EP = ET = CONST relation between EK and EP

d/c

m

A

d/c

m

B

d/c

m

C

We say that A is undamped.

We cay that B is lightly damped.

We say that C is heavily damped.

If the oscillation is stopped immediately we say that the system is critically damped.

Describe examples of damped oscillations

d/c

m

A

d/c

m

B

d/c

m

C

d/c

m

D

FYI

Without the shocks the springs would oscillate in SHM.

EXAMPLE:

The following three scenarios describe three different damping effects for the same mass/spring system.

Describe examples of damped oscillations

Undamped

(AIR)

heavily damped(WATER)

critically damped(OIL)

d/c

m

C Water

d/c

m

Oil

d/c

m

Air

x=-A x=0 x=A

Damping ref. p.43

@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

The systems and graphs we have previously looked at do not consider the effects of air resistance or friction. The amplitude

of the graph below, is (unrealistically) constant with time.

x (m)

t (s)

Damping• In reality, air resistance and friction at the point of suspension of

the pendulum will cause significant energy losses.

• The amplitude will decrease exponentially,

• … although the frequency of the oscillations will remain constant.

x (m)

t (s)T T T

@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

Degree of damping• A lightly damped system will cause a gradual decrease in amplitude

and the oscillations will continue for a fairly long time

• Damping the system more heavily will cause large amounts of energy to be lost quickly and the amplitude will be reduced to zero in a shorter time.

• In some situations, such as in a car’s suspension system, it may be desirable for the object (the car) to return to rest in

the shortest possible time without any oscillation. This is called “critical damping”.

x (m)

t (s)

The website from which the

animation came

@ Teachable and Julie Rees. Some rights reserved. http://teachable.net/res.asp?r=10075

References:

• https://www.patana.ac.th/secondary/science/anrophysics/ntopic4/commentary.htm

• http://www.teachable.net/10075-10002-resonance-powerpoint/

• http://www.youtube.com/watch?v=gQK21572oSU&feature=PlayList&p=7C51D65943955ACB&playnext_from=PL&playnext=1&index=36

• Andrew Fawcett home page of IB/AP Physics:

staffweb.mps.k12.mi.us/FawcettAM/