Fall 2003 - d‡ “ Ÿ |Œm„v fl d‡ ži |Œ“ q"...

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Unformatted text preview: d‡ “ Ÿ |Œm„v { fl d‡ ži |Œ“ q"{ kl d‡ “ |ŒmŸ { Š–l d‡ ž |Œ“ A{ opl d‡ “ €’ |Œ€‘Ÿcr¡ { Šsl ‰ r ¢ f jh hs j– ‘f d j j hs ` —d  ¨U”™“5vŒ›˜™h‡E™bq„—£hT~d†|8w • fb ps u wb `d f–x „ f `h ˜ p ub kfh– s j j ƒ r ¢ f jh hs d‡ ž ¡ „b j– ‘f  us ds t s € y dds “ „b ‘ jhxs ˆ € e„|Pv0|6g€‡—„obU6ˆc0„Aqœe†’di£hW…„X€ ž ¨GŽ’“gv†|Œ“ qi ƒvˆ›˜™h‡E’byeA„†„8` Žž 6†„”ƒvU’f‡~–ggvFzTFy i ‘Ÿ€ "{ fl i €ž "{ kl ž ‘Ÿ€ A{ Š–l yy ž e„ €y A{ opl ’ ž c“ €i A{ Šsl ‰ kf  • js “fx bh dfdds “ f `h w ‘s j w hs `h ‘ psh f `h k us u FqE6}’uv”y”g5qg„”U6g¤|™b’‘vS’‘’‘†|Fi’f6„6Œ8vU0n uff hf p u jh j „ jhs d „b h u j– šf b– “ ‚ j j “ f `h j hs ` — € “ ‘ p bx ˆ d ‚ j fx ˆ f `h “ b „ fx • f “sd f `h xf jd u b Y € qy5›w‡Pme™bœ~–goxa~–g|—›h†vWy’f‡ˆyy™6m™“F™u”T6gW’dW|8D˜0y’f6eg6Fe™bcqg6Fg–egoxagF‚ t 5”v6gƒqE’kgFea†6v d‡ “ y i u |Œm„ €“ "{ fl d‡ “ ’ € u |Œ€e‘v6y { kl d‡  u |Œ“ €‹ }{ Š–l d‡ “ ‹ u |ŒŽ € A{ opl d‡ “ ‹i u |ŒG €v q"{ Šsl ‰ u jhsx ‘f–– s d j „b f k ‚ j s “ f `h j hs ` w • ‘ psh f ` u ‘ s u jh j „ h ‚ b ` j w df ‘d u n ƒ € f b ps u wb `d d s d ˜ ‘ ‚ 8„’bgvq™fq‡ye¨™h†v†6Fg™h6u t ”†6gW’dXvF„e™fFv†6gh t e™b„ˆ„’bg‡’–ox¨Ee6g™hWq6’k’jrtA†…„Se„|Pv”|6g¨„aEy’f™‘6Fˆ f `h xf b f ˆsx k ` j ` w df ˆ bx h ‘ ˜ p kf `– shh { t y r x n t v r u n t s r p l dfdd s “ ffx `h f `h xf jd u b Y 6gq„|€Pv—E—~–6iqP„i` t ’j}ce6—„—r|s cs zU0P• cs wU0P• cGi gqonmqgge”Gy6G6†qE’kgFea†€ i €xf wd us h f d ‘ u b fd b b `– •d “ ‘ p bx ˆ ‚‡ … x b ‚ €xf wd us hdf p f `h fd b b ` y5r8v$tge™˜6eigec6—6q”y’f6„6‰vt†„Fƒy5gFvtrqPU6gigec6aY § VV¥  §© QIH #  C B @ 9  3  3 £ ¡ £ ! #   ' % # !   © §¥ £ ¡ X¨WUTSRP&GFE D¤A87)6542"10))¢(¤&$" ¨¦¤¢ €p ­ „b xf uf jhf ‘ j j j f `h ‘s ‚ ¯ jx ˆd f `h j kfx b d xf uf “ ‚ j s “ f ` ȃvŒ˜ t y6q’–‡6’uj s v~sg™h6™uUFg5~dvFqf t ’u6r€FgA™u}q„›hˆ˜ t q6yÇ6G’“E|”U6T… { fl € u j ‘ b– f `h h à d ‚ Ä ­ „b “ ‚h uf “ b “ f ` „’bg’d’j™‘e‡€6)tgXh gp WvÆ6gy”eŽUFgh „vU6Fg™h6u t ”€6gA„FgTq’f~d}e™bg~d™j’‘„y€6g(ai}’˜y|~sEq””™“j p W„Ç6eq”„”€6˜„UEFg™h6u t ”U6T… { kl b f k ‚ j s “ f `h us `h dd ‘ j u j ‘b– f `h à h … ‚ ‘fh j kf “ ­ „b “ ‚huf “b “ f `h „b f k ‚ j s “ f ` € u j ‘b– f `h h à d ‚ p ­ „b “ ‚h uf “ b “ f `h „ Âe™bg’d’j’‘„‡€Fg&†gah Ä &¨vÆ6gqŽe”U6g˜vb f6Fg™h6u t ”i6ˆ„FgXygvqx t ~dˆ„’br~d’j™‘e‡6g¤XƒtŒ’˜y|~sEq””’“†‰„Å6gqŽe”gFg†vgEF£hFu t ”g6T… { Š–l k ‚ j s “ f `h us `h xfhsf j u j ‘ b– f `h à h … ‚ ‘fh j kf “ j u ­ „b “ ‚h uf “ b “ f `h „b f k ‚ j s “ f ` € u j ‘b– f ` Âe™bg’d’j’‘„‡€Fgh h à d ‚ Ä ­ „b xf uf jhf f `h us `h dd ‘ j u j ‘b– f `h à h … ‚ ‘fh j kf “ ­ „b xf uf jhf f ` †gƒXh ap R„U˜ t y6qT’–‡6’uj s 6gŽv8gq’fƒ’dm„’br~d™j’‘„y†6g&Xƒim’˜ygv’s6q””™“j u †vU˜ t yFyT~–g‡F™uj s 6T… { opl € „ ‘ f `h bh f b “ j w p ­ dds “ f `h u j ‘ b– f `h xf „s ‘fh j kf “ ¾h‡’fU6g”te|”™‘’‘i&„”U6g}„’bg’d’j™‘e‡€6Ty¾h|}’˜y|~sEq””Á“ƒ { Šsl € h ± ° ‚ j h uf “fhs d h f tE˜iE’d†y”qg|—›h$igd ` j ` — € À h u ‚ b “s u jx ˆd f `h dfddfx ˆ “ b– uf `h u ­ dd s “ f ` … € j d ‘f ‘h– „xf ˆ j – ‘ p f `h uff hf p u j ‘ b —~–6DWSaeF„”vŒ„s t ’ugFrg6gƒrq6”„y}q6gT)a„”t6TW„’–›he’sqŽ’˜g‡qofgyPX~d¨d s E’b6t6”yqa›wy8”e™bg~d™j’‘„y– f ` … €hdfx hs ‘ j j j j ` j ` w p u ­ dd s “ s d jxhd k us ¿¦ j– ‘f  ` j w „ ‘ f `h “ b „ dxfh uf p ­ dd s “ f ` … € FTXqrq†|A™˜’‘v~sg™h6’u’d0—~–6t&­ » ‰†„””qf s gr0Fv€|ˆ›˜™h‡E’byeeg™h†¾h‡’f€6g½„oxTqgyt&ige”UFTTF“ € f ‘ „ j dh uf “fhshd fdf `h „b f u b er~dvs5~dTqŽqgvr€r6gv6e†f { fl € ¼ ´ R¶ ­ &¸ }{ kl » º´ ¹ ·´ ¶ ­ $†)A†}{ Š–l ¸ ·´ R´ r †}{ opl ¶ 2r †}{ Šsl ­ µ´ € ³f² fd b b `– • f ‘ „ fxs f u b u ƒ € h ± ° ‚ j ` j ` w h uf “fhshd h f d f `h fd b b ` Fqr0gec6—6er~dvsgvU6„F…„EtE˜iE†’dA—~–6†y”y|r$tgm6grFaY €dd ‘dd s “ j ˜ ‘ ‚ ˆ `– sf f “ ‚dd € “ jx j ‚ ¯f j ­ dd s “ f ` j ‘ b ` j ` j ` w f b p s “fhd ˜d ˜ ‘ ‚ ˆ f `h xf jd u b Y € qq’fr„”¨~d”y’f™‘F6”—„qtŽFrtW06’‚g6’p’j™‘6ˆ™u®X„”i6gh t ™uE~k„F¨~d”—’–6e|8„¬qgrEr”y’f’‘66†6¨qE’kgFea†6Ÿ M  y c’ { fl € ž€ qi 6y { kl  i v €‹ "{ Š–l i ’ €i "{ opl ž € A{ Šsl ž €d‡ “ y r «ª© §¦ • k u ‚ bd „b kff ˆd f `h „b u jh– s „ s d s xf wd us f `h f j ¥ ‰x bhbx f `h „b jh f `h „ q|Œmy  DGyqgo¨|F†F6erƒvAqq8g€6gvA„’bg‡„—oxm„y5r8v€6ie™g0œ„vU6gv0’ˆg6˜„b kff ˆd f `h j hs ` — € fh ‚ j “ xf ˆ d u jh ‘ b f yPrGFgT~dt|8DaegEc’uŽtyPTF„’bgE’‚„eyx ž   |q|—v}8v¤“ ž 6¨„TF™‚6„—”†„Ftyg6„‡~–’jy6”e„eg„g€FTT€  hs dfhshbx k us €  „b d j ksx s ds ` xfh ˆb ‘f ` s ub x bhbx f ` … TA 20 deg TD 20 deg TB TC 50 deg d‡ i vŒ“ €‹ ei “ { fl d‡ €Ÿ  vŒ“ ž E }{ kl d‡ “ €“Ÿ vŒGy 6„ey { Š–l d‡ “ i vŒG €“  v "{ opl d‡ “ € |Œm FvŸ { Šsl ‰ ‘– j ’f‡—™xy– ‘s jhxf  fh ‘ ˆ “b– s ‚bx ` j wd ‘fxs p j w p b p “ ‘ ‚ k uf ˆ f `h hs `h `– ‚ ¦ „b f ‘s “ ‚ j j “ f `h j hs ` — € „y~–ggyeg‡’f6”„y”` t „6h t ™ugG’˜yvF6’‘’‘Že8¬6’‚6EFq8Fg¨vFgm—Fgd ¿ 8„6™‚„|™6m™“F™u”6ƒ’d¨vFDƒ0“ Ÿ  6¤&ˆgh t y’fRvŽEgA£Ñ›hX` t ’jmc”qE8yPrFg¨~d”„P™F™‚66FyP†6TƒÂ„P†6g’umf t E’bWq”e‡qPXy™f’‘66†FT… Ó v r Ò ` u ‘ „b k bx j d h ‘ s ˜ p kf k uf ˆd ‚d j p b p “ ‘ ‚ k uf ˆ f ` … € p b p f `h bh j k k ‘ df “ b–f p h ‘ ‚ p f ` € t v4І„”Wvee8¤6’‚6EFq8”ˆ™ut„6g†’dm|ˆ›˜™h‡E™bq„˜v~sg™h6™ue„qg™hw t ’u|”“ t Ÿ i ϐ„”ƒviy™f’‘66zT€ ‹ Ÿ’ r ­ dds “ „b p b p “ ‘ ‚ k uf ˆ s bh j hb `d j ¿¦ j– ‘f ‘ j j j us ` j j b r n dds “ „b h ‘ ‚ p € j px b Êhx „b k jxf ˆ f `h df jh j j px b Ê j ux h „b k jxf ˆ f ` £hFgeTd rqf Ä vAE’bgq8U65q”’“gm“ i ~d£hFgead „’f6¨Wv}E™byPU6T… { fl ™h6„Td qgyf Ä „ŒE’bgq8UFgTŽ’“gm†~d£hFgead „’f6¨Wv}E™byPU6T… { kl j pxb Êhx „b k jxf ˆ f `h df jh  j j px b Ê j ux h „b k jxf ˆ f ` € j pxb Êhx „b k jxf ˆ f `h df j j j px b Ê j ux h „b k jxf ˆ f ` q™h6„Td qgyf Ä „ŒE’bgq8UFgTŽ’“gh  ~d£hFgead „’f6¨Wv}E™byPU6T… { Š–l € j pxb Êhx „b k jxf ˆ f `h f j h j j px b Ê j ux h „b k jxf ˆ f ` £h6„Td qgyf Ä vAE™byPU6ggy’–›wT~d£hFgead „’f6¨Wv}E™byPU6T… { opl € j px b Êhx „b k jxf ˆ f `h ‘ s ‚ ¯f j px b Ê j ux h „b k jxf ˆ f ` £hFgeTd rqf Ä vAE™byPU65’d„Fq£hFgead „’f6¨Wv}E™byPU6T… { Šsl ‰ h Ë Ã … j huf “fhs d h f d ` j ` — € d j ksx s hs j j pxb Ê j ux h j ` ai5t’dy”y|—›h$tg—~–6DƒŽÉ  F’‚E„—Žt|~d£h6„Td „’f6¨€’f™‘Fw É d j k sx hs j j px b Êhx € f “sdf ± s ` ‘ xshd f `h h ‚ b ps d j px b x ‘ ‚– j– ˜xs u jhs d j `hb p fxs j ux h k us hx € TF™‚6„—†|~dT™h6„5d qgyf Ä „”vqE”86™ˆtvr€656„Pv™h6„Tv~s6y’x‡ˆvFe™b|—›h0™u0vPivU’f6gX}8v†rqf Ä F € j `df– s ˆd Ê j ux h d s f jh f “sd f `h ‘h– s f j hf u ‘ ˆ f `h ‘– j– ‘ ‚ b ™ˆFr‡„8rTd „’f6gX„€”’“gg”v€6g”’˜g‡„6‡0’u†‡6„’sFU6gg’f‡—™xy}~k6„5w ˆ’6gq‡eFggd qgyf Ä ŽTvgF’‚E„—Œ€vUy6v~s6”6h t ™u£h6„"™ˆFr‡„8rUyFgvFv΄ŽE’kA¢——£hFAGy5Urqf Ä …„ƒ { fl j `df– s ˆd Êhx • É „b d j k sx s hs hf u ‘ ˆ f ` j j px b j `df– s ˆd xf `hb us u b f jx s `– j ` bh fxf w hx € j ux h u b us `h hx ub f–x „ f `h f j h ` j w dh– s f “sdf ± s ` ‘ “b „ u jh–sxhhs ‘s u jhs j s f ` e™f6¨eeA„FgTgyf Ä „‡—„ob6g‡~–›w}£h†œeUŽ„gc”F6’ˆ†Í„oxˆ„’bg‡„—gg|RvFe™b|™hcȐx t 6T… { kl € j– ‘f j ` bh ‘ ‘sxs ˆ dh–s j ux h ˜p kf– u jxf ˆ f f–x „ ‘s u jhs j s f ` „›˜™h‡E™bq„~d6”8q™f’‘v—v8TœeU™f6¨}}qyFy’fyPcy‡—„ob8vFe™b|™hcȐx t 6T… { Š–l € bxfÌ xfh fx ‘ ‚ b w ‘s–d f `h • j `df– s ˆd f `h j ‘s–d “ b bx `hs p s u b ˆf d bh fxf w j ux h FyqTygr~dj t }’k6ea’fvqg€6c’ˆ6r‡eFr€Fg}™u’fvyÇe6|FŽ0„0y›hˆty5™f6¨W…„ƒ { opl € bxfÌ j u jhsx ‘f––s Ê j ux 8gqy~dˆe™b|—y’fy‡q„d „’f6¨h { Šsl ‰ h Ë Ã … j h uf “fhshd h f d ` j ` — jhshbx hb u j hf u ‘ ˆ f `h f “ ‚dd € j px b x ‘ ‚– j– ˜xs u jhs d s atT†~dy”y|r$tg—~–6Dƒ€ t ’ugvv†vFT’d†y6v~s6U6i”6gt¨q™h6„Tv~s6y’x‡ˆvFe™b|—›h”e™uj t ’uc|”“ jb ’ˆ6gq‡eFgUŒ™u2viyFv—›h~dE€”g|qE™bX’d†’f6¨t’f’‘6„Âeg’uv6e”X›h6` t 6Xd ‡6„’s6i6gŽeb t ’uEFv—›havriFg™„ox„ j `df– s ˆd s j Év f– us j k s kfhs– ‘ j j ux h j ` w • ˆ bh jsh u ‚ b “ df j ` Êhf u ‘ ˆ f `h u j k us d xshd f `h “ b É f– us j k s hs j hx € f “ sdf ± sh f “s u hf u ‘ ˆ j j j  fx s b ` w j ux h k us hx kf “s u d j h xf jd u b Y € ŽyFv—›h~dE0U|U~dggyf Ä eŽ„gceyf Ä ”vFUy6v~s6}s t ’ug™hg’dcŽg„A6Ž’f6gX"8vUrqf Ä q”v8F™u›wgqE’kgFea†E’ €FxyqÌA„sFg5q’fT„”yyT~dŒe™b|—y’fyyy„€FgcÂ6„x t 6g}„A|6g†q”’“gR’‘v†e6‚ { fl b f u `h dd ‘ xb bxfÌ j u jhsx ‘f––s f `h • ` ˆs f `h ub u wb `d df jh ‘s x b bxfÌ j j– ‘f  f `h •d y r ¢ h yqT’dŒ›˜£hyc’byeU6gcq”¤¨†5 { kl € bxfÌ j u jhsx ‘f–– s f `h •d Ó FyqT’d}„’bg|—y’fyyye€6gcqŽŸ 6Ÿ ¼ ¢ ¼  e6‚ { Š–l xb € f jh f u j u jhsx ‘f–– s f `h •d y r ¢ h e„’gvs t F’d}„’bgvq™fq‡ye€6gcq”¤¨†5 { opl € f j jd b ˆ j j– ‘f  f `h •d e„’g™hr8†’dˆ›˜™h‡E’byeU6gcq”y ¼ ¢ ¼ ž e6‚ { Šsl xb ‰f ‘ „ j h uf “fhs d ` j ` — € fb ps f jh €d  u j jd b ˆ „b ` ˆs f `h xf jd u b Y i Èr~dvs5~d†y”y|—›he—~–6D˜e„|Pv€”’“gƒqcA„’bg™hgeP„Œ6„x t 6gTqE’kgFea€ „i 0.0 x 2.0 4.0 6.0 t (sec) d‡ “ iii vŒ€‘v€ e„"{ fl d‡ “ €’ |Œmy Ey { kl d‡ “ €“ |Œm Fvv { Š–l i d‡ |Œ“  € "{ opl ž d‡ “ vˆGy  Ÿ €ž A{ Šsl ‰ j wd j d s dd s “ f `h „b kff ˆd f `h j hs ` w • d t ’urt™hT„„”U6SvAyPr€6T~dTvF60“  ӓ ž &’dj t ’ug›h€FgvAgh t y’fU6g}F„s r Ò jx d f `h „b ` u ‘ f `h k u t s r n j “ ‘ ‚ ‚ k uf ˆ f `h „b dd s “ f `h ƒ € u jh b “ d j h ‚ b ‚ bx `h h jf ` f “ sd f ` j jsh j s “ ‘s jhxf  f ` • cG Ӟ  ÍT~dÇ6’‚666FyPU6g˜vT„”6g…„ƒÂ„’bg„”™h56„6` t „6gT` t yFg”„gU6h t ™u6’uv—™u„”cؕvq’–rq„U6h bh h–f ˆdfx ` j × ž „ b Ö us us hs ‘– j– s i‡qPrg"g™hw e „Œm™f‘ t v¢vU|m’f‡—’x‡A"’uj t ’ur¢vqÕ6’‚6EFq8g~d6gRÂgF6gyP„6Ž6gye™g€€ t ™u’j™‘q‡”6h j wd us– “ ‘ ‚ k uf ˆ j `h • `d ‚ ˆ xf ˆ bx ˆ f `h uf j ¥ jf– f ` bh kf  jx d f `h „b k uf xf `hb f `h ` j w jxhd s „ b k uf f `h u b dd s “ s • f b p s “ ‘ ‚ k uf ˆ ‘s j u b– f `h xf jd u b Y ž }qE6• t ’ug›h€FgƒvAFq†y6vU60g™h6• t ™ugr”ƒ„AFy€FgA„T„””6„e|8„Ô6™‚FEFyP†vq’–F„‡€FgqE’kgFea€ qi ...
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This note was uploaded on 04/10/2008 for the course PHY 231 taught by Professor Smith during the Fall '08 term at Michigan State University.

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