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# Free and forced Vibrations

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### Transcript

• 1. free and forced vibrations
• 2. Free oscillators
• Undamped oscillator
• Natural frequency,  o
• No external forces
• e.g. swing
• 3. 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
• 4. 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
• 5. Damping
• Resonant Amplitude limited by damping forces
• At resonance:
• rate of energy supply = WD against damping forces
• Increasing damping reduces sharpness + strength of resonance
• 6. 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
• 7. 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
• 8. Resonance and damping
• 9. 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
• 10.
• 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
• 11. 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  )
• 12. Model aircraft being tested for resonance in a wind tunnel