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p2c-s2008-lecture-1

p2c-s2008-lecture-1 - lechrei OScI'Hwtims 2 Per-fadic...

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Unformatted text preview: lechrei OScI'Hwtims 2. Per-fadic Mahdi“ {Calm-41:1 There are. Mahlg examples a'F DScI'Uai't'ms maul Pan'aell'r. Martian I‘h ha‘l'um Ramada-43 H-Fe, — Pwmrn \} f...» " +I‘cles _ arbH-s o; 'lJne Flame}: .. waves (wad-«er, sound, aqrffiquakel light) Mudn mt -Hne +erm will be gran-l: discussing Hmese Phamm-En flL Eta-Fore. discussing-Ham. we hazel-H: describe how +5 wmnc'l'erf-Ee Periodic Martian mafiemqfimfl 3 SimElt km'rmunfc Me‘l'inn (SHIN - A 519%nt kind n‘F one—Jimensl‘md (4 D) fen-radii; Martian For m kind a-p 4D Pet-India Mafia'n, an abjec‘fi‘ moves bandit aha "Fov'Hn along a 1D Pn'Hx, ann‘l'inunuslca refining 'HM'. 19qu Fur SHM, ‘Hw. object‘s Pusih‘an is :1 Sl'nusnfclad ‘Func‘h‘an err time (Sines Email-mes : "hat-manic ‘Eun cal-fans“ ) The Mn'l'iu'n up a. mass qfladucl'f'o q hnriiun'l-AJ Spring an a. ‘Frici-I'mless MIR <-———> 6b a FanMuM bub /‘ 6/ cur-e simPle. kqvmmic, Sn lung quu. nmflifltks of disqucamen't are hurt he lad-fie ' SHM and circudar Motion Circular moffm i‘s Ferr‘adfc (Wreath f-I-sel'FJ 191’?de Lira-'14? muffin 01140 an @103 l3: rsinout) 4 am As seen edge. -a-n, 1:le a-rLi-I-ing a 5hr in a aishnt swstesm QKEMQ SHM £110.?“th = radius 0" “HIE arbffi - .. SHM is EMPnrtnnt‘ Because Mama Physical Shad-ems are simple Havmcm‘c aScfllaJ-m-s - air in am organ Pipe — 'E' 25%“ fields in light "' Whom in a crash! (:41 +lne mass“ a slaving) We. Manlel Mung mPlex Stasfems as «wags up 5 im Ple hat-man I‘c as: i l la'l'ar 5 Thus consider ‘Hne Mass an a SIM-mg -—? ‘H‘xe wa‘l’lafe SHM oScflln‘l'nr When 'H'c-E, spring is uns'lre‘bked (ad.- Hs "r951: Lang-Ha“) , H' eXe‘r‘l's no ‘Force an 'Hw. mass k m k = 5‘»ng mns‘hnf x X“? I The mass is 11+ resi- at [+5 a1uili'b‘rium Fosi’ci‘m, X =¢ I-F Hue Slaring is fire-Mm}, ‘HW. mass is du‘srlqceJ in HM. Farsi-Hue X direcfi‘an . The sin-ins CXe‘r‘tS On 'Fb‘t‘ti’. in ‘H1& -X diTeCfI‘an. Sn lame: as +ke dfsPlacemeni' isn‘t ‘l-on large, "Hne magni-l-ude Ira-F Hm {at-ca is “hear-ltd Pw?u¥fl‘and +0 'Hne displacemewt k = staring cons-huff (fine Value H: k defends an haw-the sfrin is what: X=X >9 Cunshuc'l'ml: 5+? 055 a? mat-trial , urn-mi: winéihgs Perlengfimfi.) Analuawslfl. i-F Hue. slur-Eng i‘s mgresseal ‘H‘E disrlqcemen’c is in ‘Hne -X dived-fan while Hue {one is in Hue +x direcHnn m xw X=o . .3. "- 'I'kus-Pne Gan-cc law 'Fn’r (linear) swings is animwtim: Hnakells Law we. can't +|ne Same. resul+ [1‘ Ha Mass hmgs VQT‘I’I'CAI I ls 'l' . meqsunx 191mm aqul Ibrwrn “HM. uih'kn'um Paw-h" past in: — —- - 1;er an XT=JHMLEM swingii Ske‘l-MJ'fiv-m “fl-v. + +k '7‘er +|<Xn TIES M = ‘k(K1-'Xa‘ Liv-d X :-— kx \/ We cum Jehmine ‘H'IE Posfi'l'an n‘F'IJnQ ”1015qu a. 'Fund'fan a? +iV‘flE 'Frum New+m"s 2nd law _ _ day: F - ma - m ELI" = -kx 0“" 51-215; -"-‘ "' --|5 X -> 1112 e uqflm O10 d-l: m 1 mutfah pn‘tfs is. a V2113 NEH khumn EclUDs'L'l'n'n. 1+5 Sula-Hm [S x(+:) = Asin(wt +5) to E\’-"— —> deter-mime] '3 H195 rn'n Rm m i.e..lpu1m[ah~[skadnm r1“ ‘cs ass FMS -) I'mi’eg'mh‘m mafinfi, def-Ermu'ned 1M3 “Hue ini'l-i‘cd Landf’cims, fie.I big 14w, Positim a VelucH-xa a? -|Jn:z mass cut '1: = <1} The eoluwh‘an n‘F Muffin 1‘s 0. 2nd oar-Jer- JIZFFeu-enh'al afiuq‘l'inn, and Wew‘we H‘s Snluh‘an mus+ have. in: owbi‘h-wa inhgmfi'm consi-nn'l's " We, can Van-{4'3 Hid: X“) as shah above 1‘5 'H'xe Salu'l'i‘m +0 H19. aqua-Hon a? mnfl‘m his direct SubsH'hL‘Han '-' X=A§fn(w++8) lei: u; tut-+5 ' = "-Pne rhnse” 2'3; _ dx a - -> d1: .. 3|: 3% ._.._ (“if“) d(w-l:+£] I d1: Amsu. =1“ = Awmsu, dlx a? = dd; (Ammsu) = Awéflfl -Aw°l°°5“‘i& d = -Aw‘5inLL -sinu. Lu : —Aw15ih (wk +5) =—-Lu"')( v’ d1 whick is "Hie ectm‘lzian a": mo‘kimn :51 = mgx wf-H1 +1“, iden-I-ixcicai'l‘an nah—"“7 v Sn X(-t-]=Asih(wt+$) wf+‘n w=)/—m-?|I's funded “Ha-Q Salu’cian 'Fm- +‘ne PosHI‘a-n a? a mm: on a. '5??ng 9 'HH’. Fusi'l-I‘dn n-F 'H've mass is at Sl'nusui'daJ 'Fumft‘on a; +i‘me. % i‘he Mass execu+es simple haw-manic Moi-rm In -Hne 2x Pressim 51‘ Ht] 1 “Were are 3 fnmmfllms: A, nu, ma S We. haw wan-F11: examine Haw eada 641141642 Fela't‘es +a 'HW. Ma'Hn'n (“D A (“We mmrlH-udfil) since [sin (UH-+5” £1 and X= iA whan lsih(wt+$11=i , 'HWE. mmflihde E's-Hat maximum disglmemm’r a? 1+"; mass ‘Frrm {+5 eo'uu‘h'lm‘um Pusifi‘nn ® OJ (-Hwe arugula? ‘Frfiuenrifl For Hue mnmen’c, sat S=cp 9 X=Asfn(wt) Fm. PurPuses a": il‘US+Yfi+i¢n1 [at W =2“ I ah" X = A si'n (flirt) D‘r‘qw a. P|°+ n‘F X Versus '1: : X=Asmu£21rfl 1142., w did-fies haw cLufckltd 'Hné oscilla‘ct‘ms occur -) Hhe $391211ch Fa‘r 'l‘ne mass rm a. swim}, Lu = 5- lmgu k = SHFer string -? lav-(3:1- OJ ( larger res-bring firm) [away m = mare {new-Ho; —) smaller- in bu f5 callecl am cm ulwr fi-equenccfi Because H's unH-s DON: Valium/sec 1e43,} )('=A'sI'umer'L'J 6:: [mt] = am «Mia (Ham) '-7 [u] = minus/sec ([x] menus ”UhIH-s n'F x“ ) Ft‘am 'Hni's Jiswssfah , we can in‘hmauce s-I-nncImr-d +armfnulmata used +0 elem-{be osm‘llaflms The BeriaclT is 'Hne time requireJ +0 WM OWE chi-ire CJ-adfl. upmaffm (refit-n+1: ‘Hfi ihiHaJ miifims a? Fusf-l-fm 2 V‘EIDLH-ué) FM- Lu: 211 , T=1s £1“ WI=LHTJ T=%S- . .- 'Tk . a -F\- e u 3 €11.ch +‘n a am i Ple-Eacl Pa 5 an” 1r secuna [“er fiF ( [IF] mac. = Le H2) 5 0 T' DU" TE" F -2 1H=L| } F=ll 1'?- “25-4 hate Ud- JFw Tl' =21T-F w— T ...
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