free and forced vibrations
TRANSCRIPT
free and forced vibrations
Free oscillators
• 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. loudspeakervibrates 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
Damping
• 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
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 = 103
Watch quartz crystal = 105
* 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
• 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 )
Model aircraft being tested for resonance in a
wind tunnel