Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4.
Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss hrouh h rsonnc " Wor on by h forc s consu by h frcon " Enry consupon s lr nr h rsonnc
Gols for Toy " Coupl Oscllors " How pr of hronc oscllors bhv whn hy r connc wh ch ohr. " Wll us so lnr lbr " rpr for rl wvs
Coupl Oscllors " Two ncl pnulus r connc by sprn " Consr sll oscllon θ θ " prn nson s F " Rsorn forc fro rvy F sn θ F Equon of oon θ θ F F F
Equon of oon " us solv wo ffrnl quons sulnously " Bru forc " yry " nr lbr θ θ F F F
Bru Forc 0 4 4 X 0 4 X X X
Bru Forc 0 0 4 X X X X X, ± ± For ch soluon of X, w Thn w pu no X Wh pn
yry " Th wo quons r syrc " By n & subrcn h, you " W cn solv h quons for n oos l spl hronc oscllors
yry " oluons r: " How o hy loo l? B A
rlll Oscllon A B " B 0.! 0 " Two pnulus r ovn n prlll " Th sprn os nohn " nurl frquncy of fr pnulu whou coupln
yrc Oscllon A B " A 0! 0 " Two pnulus r ovn syrclly " Th sprn s pn/ shrun by wc h ovn of ch pnulu " s rn by boh h pnulus n h sprn
orl os " Th wo osclln prns r cll h norl os " Boh r spl hronc oscllon " Consn frquncy & plu " Two norl os for wo coupl oscllors " Two pnulus hv wo nl conons ch n / " Two norl os hv wo prrs ch cos bsn
Gnrl oluon " Onc you now h norl os, h nrl soluon s lnr cobnon of h. " s fn soluon h ssfs n nl conon: 0 0 0, 0 0 0, 0!! B A B A B A B A
pcfc oluon " T h rl pr: " Us cos cos cos cos sn sn cos cos cos cos cos cos β α β α β α β α β α β α sn sn cos cos
pcfc oluon.
pcfc oluon cos cos sn sn " lo shows h cs whr n r vry clos << " Th sprn consn s sll w coupln bwn h wo pnulus sll
Bs " Two oscllons of slhly ffrn frquncs prouc bs oulon of plu " Coupl oscllors chn hr plus by bs " B frquncy ffrnc of wo frquncs " Ths s us n unn pno, ur, c " Wll co bc whn w scuss roup vlocy
Fnn orl os " Is hr sysc wy of fnn norl os? " yry s usful. Bu os no lwys wor " Wh f h wo pnulus r ffrn? " Wh f w coupl hr pnulus? " W wn rcp h s urn o wor " You n lnr lbr " If you now lnr lbr, hs s n sy pplcon " If you on, sy. Ths won hur
Ch h: nr Albr ± ± ± ± 3 3 b b b b 3 3 b b b b 3 33 3 3 3 3 3 33 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Rwrn Equon of oon " W r loon for norl o " Boh n oscll on s frquncy " Throw hs no
oon for orl o " r K s vcor! consn s slf " W cll n nvcor of K " Th consn s cll h nvlu " In nrl, n n n r hs n nvcors " Brrn unforun concnc v o h " W pc o fn wo norl os hr K How?
Fnn Envlus " Equon 0 cn b ssf f 0. " Th rnn n hs cs s " Ths vs h wo soluons 0 K 0 K 0,
Fnn Envcors " For " For 0, 0 0
Bc o orl os " W foun h nvlus n nvcors. " Th norl os r vn by
Wh D W rn? " nr lbr vs you rcp for fnn norl os by solvn n nvlu probl " W sw how wor for our spl probl " I urns h h norl os s " Thr wll b n norl os f w coupl n pnulus " W cn now n our probl nown h h norl-o, consn frquncy soluons s " Ths s nouh nforon o l us c h n probl ny ny ny coupl oscllors
ny Coupl nulus " Connc pnulus wh sprns " Dsplcn of h n-h pnulu s n n,, " Equon of oon: n n n n n n
ss-prn Trnssson n " Assu h s vry lon! Inor / " Th srn jus p h ss fro flln " Equvln o ss-sprn rnssson ln n H& 4. n n n n n n n n n n n
Gon Connuous " ow w vry lr, whl n h ss n h sprn sllr n sllr " I srs o loo l sprn wh srbu ss " Goo ol for chncl wvs such s soun
ury " u coupl oscllors " Gnrl soluon s n lnr cobnon of norl os prns of oscllon wh consn frquncs " urprsn prn shows up Bs " nr lbr urns h h norl os s " Envlus! orl frquncs " Envcors! orl os " W r ry o n coupl oscllors no ss-sprn rnssson ln " Rl connuous wvs n!