10 Oscillations Notes

1 - is useful and other circum stances in w hich resonance should be avoided . (I) show an appreciation that there are som e circum stances in w hich resonance and sharpness of the resonance . understand qualitatively the factors w hich determ ine the frequency response driving freq uency near to the natural freq uency of the system , a n d (k) describe graphically how the am plitude of a forced oscillation changes w ith ü) describe practica©¥ exam p©¥es of forced oscillations and resonance. dam ping in cases sucH as a car suspensión system . to the effects of the degree of dam ping and the im portance of critical describe practical exam ples of dam ped oscillations w ith particular reference harm onic m otion. (h) describe the interchange betw een kinetic and potential energy during sim ple R esonance O scillations, and F orced D am ped H M = ilergy in and acce©¥eration during sim ple harm onic m otion. (g) describe, w ith graphical il©¥ustrations, the changes in displacem ent, v e ©¥ocity F x 2 ) . (f) recognise and use v = y o c o s a t a n d v = ÞÍ (e) recognise and use x = x o s in a) t as a so©¥ution to the equation a = - ©¡ 2 x . harm onic m otion. «d) recal©¥ and use the equation a = - ©ª 2 x as the defining equation of sim ple period in term s of both frequency and angular frequency . frequency, a n gular frequency and phase difference and express the (c) show an understanding of and use the term s am plitude, period , m ethods. (b) investigate the m otion of an oscillator using experim ental and graphica©¥ (a) describe sim ple exam ples of free oscil©¥ations. C andidates should be able to nic S im ple I Learn O utcom es D am ped and forced oscillations : resonance E nergy in sim p©¥e harm onic m otion S im p©¥e harm onic m otion content c h a UİjįȘȘ \

2 - incorporate di¨¤raction grating technology, a s a n a n ti - c o u n terfeiting m easure. engineers a©¥so create optically variable graphics (O V G ) on credit cards, w hich frequencies of light sources ranging from lam ps to distant stars. O ptical an earthquake. F urtherm ore, di¨¤raction gratings allow us to determ ine the in engineering, e . g . To prevent the collapse of a building due to w aves created by w aves, T he study and control of oscillation is needed to achieve im portant goa©¥s everyw here, e . g . iight travelling from the sun to earth, w a ter w aves and sound ©¥ife w aves consist of oscillating electric and m agnetic fields, a n d w aves are present re©¥evance to dai©¥y m olecu©¥es in a solid oscillate about their equilibrium position : electrom agnetic A pp©¥ications and O scillations and w aves play im portant roles in engineering and nature . ©¥n nature, quantum w ave - partic©¥e dua©¥ity , exp©¥aining the behaviour of m atter on the atom ic scale and understanding w r w i©¥©¥ ©¥ater be im portant for appreciating the ©¥im itation of c©¥assical physics in= historical. M any of the ideas introduced during the study of w aves in this section interference and diffraction. T he difference in the usage of the term s is m ainly superposition of w aves. H ow ever, there is actua©¥©¥y no c©¥ear distinction betw een Interference and diffraction are im portant w ave phenom ena due to the superposition al©¥ow s accurate characterisation of interaction of w aves. qua©¥itatively different w ay from how partic©¥es interact. T he pń ncip©¥e of W e can a©¥so discuss w ave m echanics, a s w a v e s intera©¢, though in a osci©¥©¥ations that do not require particles. that e©¥ectrom agnetic w aves can trave©¥ through a vacuum , a n e x a m ple of field attendant transfer of m atter. R em arkab©¥y, o n e o f the m any surprises of nature is disturbances far aw ay . W aves are a m eans of transm itting energy w ithout the oscil©¥ations then spread out as w aves, w hich carry energy and can resu©¥t in continuous m edia. A ©¥l w aves are disturbances w hich result in oscil©¥ations. T he W ith w aves, w e m o v e c o n c e ptua©¥ly from physics of particles to the physics of Wequally fundam ental for describing and understanding the physical universe. turns out that the w ave picture, generalised beyond classical m echanics, is «¤国 ûö w ithin the system . W hile w e have seen how pow erfu©¥ the particle picture is, it undergoing oscillations is the starting point that leads on to the idea of w aves W hen w e consider a system of connected particles, the idea of single particles kinem atics, dynam ics, forces and energy in trying to understand S H M . describe m ore com plicated oscillations. N aturally, w e re v isit concepts in uniform circular m otion, a n d provides a m athem atical basis upon w hich to m otion (S H M ) . S uch sinusoidally varying m otion is essentially a projection of the m athem atically sim plest case of » ee oscillations, know n as sim ple harm onic N onetheless, w e c a n gain a deep understanding of periodic m otion by analysing spatial dim ension, there can be com plicated types of periodic m otion. have studied uniform circular m otion, w hich is periodic and regular. E ven in one equilibrium . W hile m uch of the m otion w e have considered is non - periodic, w e and arises for exam ple w hen objects are perturbed from a condition of stable P eriodic m otion, w here the pattern of m ovem ent repeats over tim e, is ubiquitous, sections and Topis L inks B etw een 10 . 0 1 0 sci©¥lations and W avesgļ : ￠% j©©eĤ į jg$ ģ āę ñ Ē ' ©© # ? i©¥į ç ©© ' \î f . W¡×U Ëjf' Į ': - . l Y r 5 - 6 P H Y S ©¥C S D E P A R T M E N T R A F F L E S ©¥N S T IT U T ©¥O N

3 - energy conservation of obeys the interference pattern doub©¥e - s lit distribution of a T h e int en s i ty source distance for a point betw een intensity and T h e re©¥at ion s h i p an S H M system m echanica©¥ energy in C o n s e r va t ion of C onservation L aw s attenuation) and air resistance (negligible ignore dissipative forces like friction S i mp l ifyi ng as s u m p t ion s e . g . graph (snapshot of w ave in tim e) partic©¥e) , disp©¥acem ent - position tim e graph (characteristic of every w avefront diagram s, displacem ent - co m m o n rep r es e n t at ion s : e. g . interference, ditftaction) (e. g . s tanding w aves, tw o - s o u r c e used to explain w ave phenom ena * S u p e rp o s itio n p rin c ip ©¥e , w hich is radiation W a v e na t ur e of e©¥ec t rom a g n e t ic * M e c h a n ic a l w a v e m o d e l displacem ent that is proportional to its characterised by a restoring force S i mp ©¥e ha r mo n i c mo t ion of a ma s s M ode©¥s and R epresentations scatteringj diffraction, a bsorption, reflection, r e fraction, w ith m atter (e. g . . , e©¥ectrom agnetic w a ve I nt er ac t ion of and space m om entum through tim e transfer energy and disturbance that can * A w a v e is a s o u rc e o f S ystem s and Interactions L inks to C ore ©¥deas Y r 5 - 6 P H Y S IC S D E P A R T M E N T R A FF LE S ©¥N S T ©¥T U T ©¥O N

velocity, w h©¥ch ©¥s the rate of change of angular displacem ent. frequency . W hen dealing with uniform circular m otion, a ) s ta nds for angular not the sam e, W hen dealing with sim ple harm onic m otion, a ) s ta n d s for angu/ar have the sam e units of rad s ' ' a n d are w ritten w ith the sam e sym bol a), they are D o not confuse angu/ar frequency w ith angular velocity . E ven though the two usual kinem atics equations in solving S H M problem s. S ince the acceleration of the object is D gţ constant, it is not possib©¥e to apply the direction opposite to that of the disp©¥acem ent x. T he negative sign in the equation indicates that the acceleration a acts in a T he unit of (o is radian per second (rad s - ' ) . n Jl oscillation, a n d is equal to the product of 2 rr and its frequency (i e (o - 2 rro rl A ngu©¥ar frequency is defined as the rate of change of phase angle of the and a1 2 is a positive constant, w here a) is the angula