uebung5 - T0 x êë T0 ìí nìí u0 = 0 î èé nnnnèé...

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Unformatted text preview: T0 x êë T0 ìí nìí u0 = 0 î èé nnnnèé èé èé èé êë îï èé nnnnèé èé èé èé êë ï é é é é ènènènèn nnnnèé d é é é é ènènènèn nnnnèé èé nnnnèé èé èé èé êë èé nnnnèé èé èé èé êë T1 êë èé nnnnèé èé èé èé d êë T1 r u1 = ω r y ω —{ 3Qv x„ qfsffŽq1s|““yQwçGmfqw¤#qÂÀB›“fqä „ l ~ u ¤ l p k ˆ  ˆ x k v x r v{ z p u Ù x  É — æ å à㠈{k  } ˆ xk ||syQymiPymwwG•”¬wfs|““qwu Š ‰ xk u ˆ v r r Þ x x l pk ˆ  ˆ p 㠗 Š— #§â§„ l v€ t  u v   ¡ Q‚ÄqeyQsq1ÎqAm{ r x zk x x v u t mywGwf•sqBm§{ r p o lk ¤Ò }  l ~ ˆ Š ‰k Œ à fffw©PmAáfÜ|Ófqßyq©mwBsmwßyfq“¸Ì lk l k u  Í lk x l pk ˆ { x l  u rvˆx Þ Ã G“y¬¬ÖqYÂcÝÕGQm5Äs“©PQyÜBQmy¿¨ÜqP|#ÖGf’|YÄà x„ É — Å v k o à vˆ Š‰vu v Š vk xÁ Ë v o ‰k É uv„ ˆ{  t lv „uv QBq“Gs»GsfqmcPm|ffQBf”|qÈQywQB“w½Pyx l v  l { Š ‰k{ „ l v l ~ x{  lvxxv „ˆˆˆ l v ˆ  lk „ u p p o u { p Ù G“fmfysĐwqmscm'©PmBl lk ˆ Š ‰k r v{ z p u Ù Gmfsy¤qYG“©Pqw“‡$ciÛGwfTÈGffPGwu x„ ˆvˆ Š‰uˆv z l Ú —xx ~ r lv l Š‰v r v{ z p u Ù Gmfqw¤qfcq”wqfw3Gw“Ø x„ l r xx „ px }kvx × Ç'yqY§qÖmAcG”fGfl Ë xx „ } l uk ¥ lv rŠv } l v Š ‰ € lk v u v Í §GfPq¿B|QyQsGqBf5fPQA¶mB¢Ž°Õ$œGwu|qYPwyQs¸#Qf#B“wQv ~  l ~l Š‰v  vk „ r‹ —Ô Ï kvx v{  Š ‰ x u v   ¡ u v „ u ~ ˆ  u ¤Ò xv „ Ð Ï u ~ˆu QfÑ19f“½“Qv t ”G°m#Ó§G”•mwyQv rv Ì vk É — l v r rk ˆ x z t •Q¸ÂmfÂ|AWyÎ|YyGm•fPĦGf'mBqmwQqyfw“G$•Q¸Ì r v Ì vk „ vk ¥ p x r{ † u vk r Š‰ à rv„ lk € ~ { u v Í u ~ ˆ  u v t rv lv„ QBÈB¬¨Gm|sy•mǛYqP|#ÊQf„ l~l l v{{ p ¥ uk ˜ —Ë v o ‰k É uv r{ † u vk mfyQ|”BPÄÈmGÈP|wfBYGv r Š‰ à lk v Š ‰k x v„l† v{  Š ‰ x u v   ¡ u v „ |qYPwyQs¸ÆGf”GfPw|A$ƇeQQ|5Ďqf|mAfGmw‚‡“©Pqw“Gv l v Š ‰ xk ¥ ž — Å v k o à v o lk{ v Š vk xÁ ˆ v ˆ Š ‰  u ˆ z ÇQ‚BqQwGsq1¡ l v€ t  u v   z u v   ¡ x v ˆ v ˆ x { ¤Qqq1yG“GwyqmQv rv„ GfÇff~ „l zl~ 5f’mQÀfwGy¤¤j lk v v „ u v ¥ x ™ · — ´³ g¾ g ¸¸W7¬¿¬š½f†»¸š¸¸œ‚¬¶7'5f¦°§“¤f@1'– ² ± ¼d º ¹·— ™ · — e³ g µ ´³ ² ±g™d¯ ®­ g e d ™˜ — L g z=0 z(t) — l v ~ « v u ƒ v x vk „ v{ ˆ ˆk fQB¬GwY‘wGmf#|“y|•w¤y8Qsf|A©Pwx r u j — l v  lk ¥ Š ‰ lv ~ «vu ƒ fGf5QwYªQfPym“myQ“©qwqYP¨GfmG¨|•§G¦wmAQyw¨mGw‚£sq1¢QwyQ|QGm5wŸff5fP|Q8ž l v Š ‰ xk ˆxk u v ˆ o  u  Š ‰ u v lk v ˆk r xv „ uk ¥ } ˆ x x ¤ { k v u € v¡ l v ˆ u vk k o x  l ~ l Š ‰k v uv„ Gf›mQff›mf|œ“qY›q”•fGš™Qym”Q$q•Qff¤”QBmQv lk uv„ x~ „k ~{ ƒ x„ l r llv ˜ — ˆ xk lv –p lv„l j l v „k lvˆ lˆx l po Qw5PyBsqfqŽ¨A‹ u Š p Œ z ”q“qY’Qww|BfPwyQf~ l x„ } x ˆ ˆk l Š ‰ x u v ‘ r v lk v GfmGnmnPmy‡ffY‡$…|fmiQmGw‚sfff|Qy'QQ|fmywGwf•sqBmnm¤j lk Š ‰k x ˆv „ l †v z „k ~{ ƒ x vk v u€ x  l ~ zk v u } x v{ zk x x v u t r p o lk lk h i¤f@1'– g e d ™˜ — ’ •“'”“'‘ssd ’‚ € ’‚ €‰ ˆ ‡ p ƒ … †„ ‚ 'yw € x v ef ` D XH [email protected] t usqiQeca r p h g gf db 6 ¥ [email protected][email protected]) 6 0 ! 6 4 2 0 ) R 0 D HF DC ( 6  6 0 ! 6 4 2 0 ( ¢'$#¢© & % ¡ " ! !  © ¨§¦¤¢    ¥ © ¥ ¥ £ ¡ Technische Hochschule Zürich Politecnico federale di Zurigo Swiss Federal Institute of Technology Zurich | o– h o ¼ e • ’© g– º i s o j ’ |™ s s–g | h | v v v ¹ ¬ s ’ – eg – }‡ œ ” ž ‰T4‰ŸW4wo4˜4¨»„Tf–‹†ƒ˜¤©f’T¤–&|5r}El r•Fxx‰[email protected]4af¦ƒU¸µ·˜¯ iT4¶m4˜¨‹‹U‚o ‡ µ4†…„‚ ƒ 4…$‰†´44T˜r–TU‰³†…±TŒU&‡¤•5mU€€T°r–wyT®¤jU­p…rqTX‹wokœ –h ljg i’¯ s o ¢ eo j™ ij™ h o j eojq yi‡ ² i j™ o– o sg }i‡lo¯ y– s¢ — ¬ •– v • « o– hi– v o–™– – ™ g sgig –q ’© jg o– o ¢ o–™ g elj £ ¦j ¤£ • }g o h • y ‰T4nTX¢TT…4&e4feªnaf¦„˜‹¨TŒ‹U‚o ‡ §TTnmk¤—‰¥mUr¢~‰¡¤h4zjŸž &–” "œ ¦$4T•TrqT˜k—T48UhT•TU”“ w}$4C‘¤QpŽ 4&gTuTŒ‹UŠ74‰T4ˆeU€l • | Ž  › š ™ o–s •qq — i– h i ‡ – o–sq g • i ’ ƒ  | } j e sqi– o o ‡ ” – h o– y ‡ e o j™ i– h i– h •– v– s • • }i s–™ g ™ | • •–il s • o–™ g elj — i– h –™ g ™ — • 4†…„‚ ƒ T4†T4sqwyTXT€tTrqwwo~mTf–TTfed— {ez•wywyxwvTumtTrqpTTnmk˜T4†Tfed˜&–” T0 ˆ‰ T0 x ˆ‰ ˆ‰ ˆ‰ d ˆ‰ ˆ‰ †…†…†…† ‡‡‡ …‡††††…‡ †…†…†…† ‡‡‡ …‡††††…‡ †…†…†…† ‡‡‡ …‡††††…‡ †…†…†…† ‡‡‡ …‡††††…‡ †…†…†…† ‡‡‡ …‡††††…‡ †…†…†…† ‡‡‡ …‡††††…‡ ‡‡‡‡ …†…†…†…† ††††…‡ u0 = 0 d u1 = ω r T1 ˆ‰ ‘ † †‘ ’“ T1 r y ω P „U ƒ $ y % e ‚ €G x R v¤e "usra q e ! rw g At ` H ig phfe Sc a db` 9 Y # X £ £  £ W 2 V RPI R PI  VUT! 9 S  CQE! 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[email protected] &¥ 8 76 542 1) (&¥ $   " — u v lk v GfmGcff~ „l å  å Ø ”BmfqŽ x ~k „  r v lk v k QBmQŽQv ˆk |•¤Qww|•wGm•fPĚmG‘Bݑ8 r { v ˆ ˆk r u vk r Š‰ à l k v u ¤~ € Ô Ï z ¶Å ä  Áä Bf æ ÐÏ 1’fQyQ$|fyf“wQv l v u v –k „ u ~ ˆ  u ææ sq å å { Š x l ~ Švu „ fqQwsfB¬Gwf•À‹ r „l~ ff’ Å Áä f å u qAssBf•§’ Ëä ÏË „l~ æ å ÏÁ ‚¦ u ¤~ € Ô Ï fPÀ$ÈȤ å Ï xx „ } lv yqY¸§Q•fQBfq“q”r rŠvll l llo} f1s æ E Á  Ë À æ t ”G•mBšf5°ym‘wqws’mǘ rv Ì vk „ l~l ˆ xk x x p u  vk — YË u ¤~ € fP’æ Å „ å ¶ l v  l ~  lk „ v z „ l   GsffsBmfG$fBqÀÜQBfQs|s‚ÊQfAV”fw“G$t l v „ l v { p€ l v „ ˆk r u ~ˆuv Œ ¶Q¸u|f#fÝÂ3s#u“Gw|GmQqfq#ÂG“©f¶mB“B¬¶ysƑe||sÀ rv Ì v k „ u ¤~ € — {  É v ˆ v ˆk v{ v  z  Å z u v ˆ l ~ vk „ l~l v x ¤p ¡ — ˆ { k  å #Å × °$½w‡$ Ô ÏäÅÔ Ï å ÀÅ ÏÁ 7 „l~ ffÀ Ð ÏÁ 1‚»Š 8fBfuw°y¤’fmGm5#f¤ ~ —„}l~ r u ¤ ¥ u j v lk v{ o u — Š ‰ k {  ¤p §P|mssiÓmAA|GyÕyyÝ©Q|Q• ¬qysffw|Q|Q•wq•˜ r vk ¥ ˆk v ¥ p x Å ˆ l vk v p o x  l ~ ˆk v{ v r u ¤ ÅÏ #¶5 ¬ Ë Ø Œlj ¬¦•|fÂfP'ff5PmGm{ v k „ u ¤~ €  l ~ Š ‰k v Ë À å å ƒ ŠՉ Á Ï • l~ fBusÕw¬ŽQ|fmywGwf•sqBmÊm¶fB“|YwGQmqwQv r ¤p u ˆ à u v { z k x x v u t r p o lk lk  l ~ ˆ{  Š u v vk  u §¥ ¨ ¤£ ¦  §      ¤£ ¢ ¡ vk „ |fšB¬•fPq¿ÄmQyQ¦ l~l v Š ‰ € lk v u v Å B$ Á „l~Å ffÑB  Á æ Î äÏ ” ˆ{k  Vms“ffyu „l~ lvˆlv lp t G“©Qfq$•sqy“VQqqmff|A©PwQv r p o x ˆk v o k „ lk ¥ Š ‰ x © r v Š ‰{ v ¥ x QBPmQÑÂf~ vk „ mBqG“BßÂmǘ l v ˆ ~ { vk Å z Å © ...
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This note was uploaded on 03/15/2012 for the course MAVT FFD01 taught by Professor Roesgen during the Spring '00 term at Swiss Federal Institute of Technology Zurich.

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