2. © John Parkinson 1 VIBRATIONS & RESONANCE

3. © 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.

4. © 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”

5. © John Parkinson 4 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

6. © 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

7. © John Parkinson 6 Other Resonance Examples RUMBLE STRIPS 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. Bus windows At low engine revs the windows natural frequency can be the same as that of the engine.

8. © John Parkinson 7 Tuning Circuit 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

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

10. © John Parkinson 9 applied frequency amplitude Resonant frequency f 0 RELATIONSHIP BETWEEN AMPLITUDE AND DRIVER FREQUENCY LIGHT DAMPING HEAVY DAMPING

11. © John Parkinson 10 Phase lag in degrees f0f0 0 180 90 Applied frequency Phase lag of the driven system behind the driver frequency

12. © 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.) slight damping

13. © John Parkinson 12 time DAMPING DISPLACEMENT INITIAL AMPLITUDE THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME

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

15. © 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 Direction of travel VIBRATION

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

17. © John Parkinson 16 transverse wave

18. © 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!!) Direction of travel vibration

19. © 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

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

21. © John Parkinson 20

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

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

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