# VIBRATIONS

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By: charles31220 (68 month(s) ago)

plz sir i need this for my seminar at coll

## Presentation Transcript

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© John Parkinson 1 VIBRATIONS & RESONANCE

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© John Parkinson 2 Natural Frequency / Free Vibrations the frequency at which an elastic system naturally tends to vibrate, if it is displaced and then released The natural frequency of a body depends on its elasticity and its shape. At this frequency, a minimum energy is required to produce a forced vibration. Free vibration is the vibration of an object that has been set in motion and then left.

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© John Parkinson 3 Forced vibrations are the result of a vibration caused by the continuous application of a repetitive force Unless the forcing frequency is equal to the natural frequency, the amplitude of oscillation will be small. e.g. a swing pushed at “the wrong frequency”

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© John Parkinson 4 RESONANCE the result of forced vibrations in a body when the applied frequency matches the natural frequency of the body The resulting vibration has a high amplitude -- and can destroy the body that is vibrating. Resonance allows energy to be transferred efficiently

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© John Parkinson 5 ON NOVEMBER, 7 1940 THE TACOMA NARROWS BRIDGE IN WASHINGTON STATE WAS BUFFETED BY 40 MPH WINDS AT APPROXIMATELY 11:00 AM, IT COLLAPSED DUE TO WIND-INDUCED VIBRATIONS http://www.civeng.carleton.ca/Exhibits/Tacoma_Narrows/ http://www.glendale-h.schools.nsw.edu.au/faculty_pages/ind_arts_web/bridgeweb/commentary.htm WATCH A VIDEO AT OR AT

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© John Parkinson 6 Other Resonance Examples Wheels hit the strips at regular time intervals as the car travels at a steady speed and this makes the suspension resonate so the car vibrates with a larger and larger amplitude and makes the driver slow down. At low engine revs the windows natural frequency can be the same as that of the engine.

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© John Parkinson 7 The circuit contain the coil and the capacitor resonates to a certain frequency of AC that is picked up in the aerial. The variable capacitor enables different frequencies to be received A wine glass can be broken by a singer finding its resonant frequency

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© John Parkinson 8 DRIVER FREQUENCY IN PURPLE DRIVEN FREQUENCY IN ORANGE

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© John Parkinson 9 applied frequency amplitude Resonant frequency f0 RELATIONSHIP BETWEEN AMPLITUDE AND DRIVER FREQUENCY LIGHT DAMPING

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© John Parkinson 10 Phase lag of the driven system behind the driver frequency

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© John Parkinson 11 Damping Damping is the term used to describe the loss of energy of an oscillating system(due to friction/air resistance/ elastic hysteresis etc.)

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© John Parkinson 12 DAMPING DISPLACEMENT THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME

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© John Parkinson 13 With Critically Damped motion the body will return to the equilibrium in the shortest time - about T/4.

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© John Parkinson 14 Longitudinal Waves Each point or particle is moving parallel or antiparallel to the direction of propagation of the wave. Common examples:- Sound, slinky springs sesmic p waves Longitudinal waves cannot be polarised

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© John Parkinson 15 A longitudinal sound wave in air produced by a tuning fork Observe the compressions and rarefactions

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© John Parkinson 16 transverse wave

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© John Parkinson 17 Transverse Each point or particle is moving perpendicular to the direction of propagation of the wave. Common examples:- Water, electromagnetic, ropes, seismic s waves You can prove that you have a transverse wave if you can polarise the wave (especially important with light (electromagnetic) as you cannot “see” the wave!!)

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© John Parkinson 18 Formation of a STANDING WAVE Two counter-propagating travelling waves of same frequency and amplitude superpose to form a standing wave, characterised by nodes (positions of zero disturbance) and antinodes (positions of maximum disturbance

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© John Parkinson 19 Node to Node = ½ ? BETWEEN ANY PAIR OF ADJACENT NODES, ALL PARTICLES ARE MOVING IN PHASE

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© John Parkinson 20

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© John Parkinson 21 STANDING WAVES ON A STRING Fundamental length = ?/2 First overtone length = ? Second overtone length = 3?/2

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© John Parkinson 22 LONGITUDINAL STANDING WAVES OPEN ENDED PIPE FUNDAMENTAL l = ?/2 1st harmonic actual air vibration 1st overtone l = ? 2nd harmonic 2nd overtone l = 3?/2 3rd harmonic

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© John Parkinson 23 CLOSED PIPE FUNDAMENTAL l = ?/4 1st harmonic 1st overtone l = 3?/4 3rd harmonic 2nd overtone l = 5?/4 5th harmonic