lassiiaio/lidiesioal PEs Mah 9 lassiiaio o PEs ad Mlidiesioal PEs a aeo Mehaial Egieeig 5 Seia i Egieeig alsis Mah 9 Oveview Review las lass Wave eaio solios b seaaio o vaiables ad lebe aoah haaeisis ad lassiiaio o aial dieeial eaios Geeal aalsis Paaboli eaios Ellii eaios eboli eaios Solvig a wave eaio oble Mide Ea Wedesda Mah oves aeial o disio ad alae eaios Ildes aeial o ad ildig oigh s Feba 3 lee ad hoewok o Moda Mah Oe book ad oes ildig hoewok solios Fos o wokig wih eig solios 3 Review Wave Eaio Usal assio Resl is io o eal o io o os [ os ][ ] Use above solio as saig oi oda odiios a ad Iiial odiios o ad / a Review Geeal Solio Solio o wih iiial ad boda odiios ; / g is wave seed g d os d 5 Review Use o ig Ideiies os os os os os os os 6 ME 5 Egieeig alsis
lassiiaio/lidiesioal PEs Mah 9 Review lebe Solio Wave heoea: is wave alide vaig wih sae ad ie is wave seed Ove a egio ad lebe solio g ξ ad η ad / g [ ] gν dν Review labe II We see ha he solio obaied b seaaio o vaiables agees wih he labe solio o oe ase Solio shows oagaio o wave shaes wiho daig ook a eaig o ad s ie ieases eais he shae o he iiial odiio ad oves o he le Siilal eais is shae ad oves o he igh 7 8 ie Review Wave Poagaio 3 - - Review odaies Wih g solio is Foie e seies whih is eiodi odd io.5 -.5 - - -.5 - -.5.5.5 Peiodi eesios al solio -5 - -3 - - 3 5 disae 9 5 3 5 Review ie Evolio ook a evolio whe..5 -.5 - /./ Iiial odiio - -.5 - -.5.5.5 Fo lage vales o eiodi eesios ove io -/ -./ -.5.5 -.5...6.8.5.5 -.5...6.8.5.5 -.5...6.8 Phase behavio o e io ases iiial wave o o be eleed a bodaies ME 5 Egieeig alsis
lassiiaio/lidiesioal PEs Mah 9 ME 5 Egieeig alsis 3 3 Review haaeisis Used o lassi seod-ode PEs d d alsis gives sloe o haaeisis haaeisis sloes gives egio o ilee ad doai o deedee Review lassiiaio o PEs he geeal seod-ode PE i wo vaiables is lassiied as ollows I < he PE is alled ellii ad has o eal haaeisi dieios I he PE is aaboli ad has oe eeaed haaeisi dieio I > he PE is heboli ad has wo eal haaeisi dieios d d 5 alae/poisso/elhol eaios < ae ellii o eal haaeisis isio eaio > is aaboli oe haaeisi Wave eaio > is heboli wo eal haaeisis 6 Wave Eaio haaeisis oe haaeisi dieios Wave eaio: ; ; ; > d d 7 Wave Eaio haaeisis II oe haaeisi dieios wih ode o vaiables evesed Wave eaio: ; ; ; > d d 8 Review Wave Poagaio -5 - -3 - - 3 5 disae ie 3 - - haaeisi sloe d/d / haaeisi sloe d/d -/
lassiiaio/lidiesioal PEs Mah 9 ehavio o Eaio es oai o deedee o he aea i - sae whose vales ae he vale o Regio o ilee o he aea i - sae whose vales ae aeed b he vale o Ioae o seiig boda odiios ad o eial solios e-ig haaeisi d/d < Iiial odiio ve oai o deedee Righ-ig haaeisi d/d > 9 eboli Eaios oai o deedee show o evios ha Regio o ilee is egio o haaeisis leavig odiios oside doai o deedee shold o ae solio Ioa oi o eial algoihs whih a violae his iile o iaoiae hoies o se sies Ellii PEs Iagia haaeisis o ellii eaios like alae ad Poisso s Eie solio egio is boh doai o deedee ad egio o ilee Ms have losed bodaies his eas ha a hage i a boda odiio a ae he solio a a oi i he egio Ees a be sall a o boda b will be ese Paaboli PEs Paaboli eaios iall ivolve ie ad sae as oodiaes oside egio ad > oai o deedee a a oi is eie doai a evios ies: ad < hage i iiial odiios o boda odiios o < will hage solio hee Regio o ilee a is eie egio o e ies ad > Eale Qesio o ae solvig he disio eaio i he egio ad > wih a iiial odiio ad he ollowig boda odiios < s: s: a I o have a solio o his oble o a how does he solio hage o < s i o se a? 3 Wok o oewok Poble Page 57 oble solve he wave eaio o ad wih boda ad iiial odiios show.. Sa wih seaaio o vaiables esl [ os ][ os ] ME 5 Egieeig alsis
lassiiaio/lidiesioal PEs Mah 9 ME 5 Egieeig alsis 5 5 Wok o oewok Poble.. [ ][ ] os os Fo we s have Fo we s have a iege 6 Wok o oewok Poble [ ] os Fo solio o a ad we have o g d g d I his oble so we have all 7 Wok o oewok Poble d g Use io give o g o ge.. d d Se ad 8 Mlidiesioal Eaios a have eaios i hee sae diesios ad ie lassiiaio as ellii aaboli o heboli does o al o eaios wih oe ha wo diesios oodiaes a have ellii-like aaboli-like ad heboli-like behavio i lidiesioal eaios E. g. ie is a aaboli oodiae 9 Mlidiesioal alae Geeal alae eaio o hee diesios Shee lidial aesia o 3 Mlidiesioal isio Geeal disio eaio o hee diesios Shee lidial aesia o
lassiiaio/lidiesioal PEs Mah 9 ME 5 Egieeig alsis 6 3 Mlidiesioal Wave Eaio Geeal wave eaio o hee diesios Shee lidial aesia o 3 Phsial Soe es Poisso Eaio is alae s Eaio wih a soe e S S Soe e a deed o oodiaes o ø ad a have siila es i disio eaio ad i wave eaio S S 33 Mlidiesioal Solios wo-diesioal disio eaio o Use seaaio o vaiable aoah wih all vaiables 3 Mlidiesioal Solios II Seaaio o vaiables woks eah e s eal a osa 35 Mlidiesioal PEs II ave 3 OEs wih kow solios os Ee os 36 l oda odiios > gives ad gives / so / > gives ad gives / so / Ee -[/ /] / / eigeio eie osa as E
lassiiaio/lidiesioal PEs Mah 9 ME 5 Egieeig alsis 7 37 Iiial odiio Ge geeal solio as s o all eigeios ad ge iiial odiio e Mlil b [/ /]dd ad iegae o ad 38 Iiial odiio Gives d d dd dd Use ohogoali o e ad evios esls o iegals o ge dd