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Free And Forced Vibrations

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Information about Free And Forced Vibrations

Published on March 24, 2009

Author: christaines

Source: slideshare.net

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free and forced vibrations

Free oscillators Undamped oscillator Natural frequency,  o No external forces e.g. swing

Undamped oscillator

Natural frequency,  o

No external forces

e.g. swing

Forced oscillators External forces act on oscillator Forced/driven oscillator Resonance: driving  =  o e.g. loudspeaker vibrates in response to oscillating electric signal (driver) Barton's pendulums

External forces act on oscillator

Forced/driven oscillator

Resonance: driving  =  o

e.g. loudspeaker

vibrates in response to oscillating electric signal (driver)

Barton's pendulums

Problems Resonance driver applies forces that continually supply energy to oscillator  increasing amplitude A increases indefinitely unless energy transferred away Severe case: A limit reached when oscillator destroys itself e.g. wine glass shatters when opera singer reaches particular note

Resonance driver applies forces that continually supply energy to oscillator  increasing amplitude

A increases indefinitely unless energy transferred away

Severe case: A limit reached when oscillator destroys itself

e.g. wine glass shatters when opera singer reaches particular note

Damping Resonant Amplitude limited by damping forces At resonance: rate of energy supply = WD against damping forces Increasing damping reduces sharpness + strength of resonance

Resonant Amplitude limited by damping forces

At resonance:

rate of energy supply = WD against damping forces

Increasing damping reduces sharpness + strength of resonance

Types of damping Oscillating masses lose energy  amplitude decreases Light damping: amplitude decreases gradually Critical damping: amplitude decreases can decrease to zero without oscillation. Minimum time = T/4

Oscillating masses lose energy  amplitude decreases

Light damping: amplitude decreases gradually

Critical damping: amplitude decreases can decrease to zero without oscillation. Minimum time = T/4

Q-factors Measure of resonance Definition: number free oscillations a free oscillator competes before decaying to zero * Light damping = large Q factor Heavy damping = small Q factor e.g. Car = 1 Guitar string = 10 3 Watch quartz crystal = 10 5 * This is only an approximation. Q-factor does have a complicated precise mathematical definition

Measure of resonance

Definition: number free oscillations a free oscillator competes before decaying to zero *

Light damping = large Q factor

Heavy damping = small Q factor

e.g. Car = 1

Guitar string = 10 3

Watch quartz crystal = 10 5

* This is only an approximation. Q-factor does have a complicated precise mathematical definition

Resonance and damping

Examples Pushing a child on a swing – maximum A when pushing  =  o Tuning a radio – electrical resonance occurs when  o of tuning circuit adjusted to match  of incoming signal Pipe instruments - column of air forced to vibrate. If reed  =  o of column loud sound produced Rotating machinery – e.g. washing machine. An out of balance drum will result in violent vibrations at certain speeds

Pushing a child on a swing – maximum A when pushing  =  o

Tuning a radio – electrical resonance occurs when  o of tuning circuit adjusted to match  of incoming signal

Pipe instruments - column of air forced to vibrate. If reed  =  o of column loud sound produced

Rotating machinery – e.g. washing machine. An out of balance drum will result in violent vibrations at certain speeds

Investigation strength of chemical bonds – EM radiation = oscillating electrical disturbance. When incident on a crystal ions subjected to oscillating electrical force. At correct frequency ions ions oscillated by resonance Energy is absorbed from radiation, the frequency of which can be measured with a spectrometer

Investigation strength of chemical bonds – EM radiation = oscillating electrical disturbance. When incident on a crystal ions subjected to oscillating electrical force. At correct frequency ions ions oscillated by resonance

Energy is absorbed from radiation, the frequency of which can be measured with a spectrometer

Unwanted resonance Structures/machinery Results in destruction Damping Changing  o of object by changing its mass Change stiffness of supports (  moving resonant  away from driving  )

Structures/machinery

Results in destruction

Damping

Changing  o of object by changing its mass

Change stiffness of supports (  moving resonant  away from driving  )

Model aircraft being tested for resonance in a wind tunnel

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