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1 "!# $&%('*),+ -*%(. -0/,1 '#'#243,5"%768249 :;5<->=<= 2?/,-A@B-*9 -#: 5 28'H1I JLK NMO J P P QRTS7U V<W?XY Z [ \ ]_^ a`bMc!# !# d 7 eM `b`#Mf g Lh i ; jb !bMf jk M j# MO!*!b jb BMO lMe j#jkMnmo F eM `b`bMfpTq r sQ 1024t "uv h M a kw x !b B y z"i Mc!b jb e!# j#jb `*!#jb {| } L a Mn!#jb c~cMOjk`* `* 0h j# x`*i lM ~ j*!b MO B vi `H!b `b`* nh i "!# M`#i h j# N !# j#jb `*!#jb Lm jb !bM0 `*!bM M j# lM us\< &] MO l M j# , ;jkMO y jb !kMs o 7 o 7 Y,Z [(\\< &] < v jb !bM v `*!bMO MOjb lM { h jb < j# ~ i v `bMc!b !# v vi i MO &M z"i jb O!kMO lM j#jkM { T JO wr q I P`s Me j# MB jbM ~< !b e 0i MB jb MA !bjbM { `* `* j#~cMAz i 7 L L "!b AMO lMOjb { h jk A`# d | L O!# A jk M j# 7 0 i x MB~ !b B `*!bMO "!b s M jkMO w MBz"i |`# B lMB LhN "!# jb LM s jb ~ lMLh jb eM0 z"i M M jb M jb jb LM `# ;w M m!2R=GMTmR2 c~ !qJ T z"i ; jkMO L y j# !kM R= (GMT!2)1=3 42168Km:Y Z [ ] ^ j#h e ; eM `b`bMd qJ 0 M h hN MO!))}}}}

2 # LM Ai ML L ML LM `#`bMd!#jkM `b i jkMO , `*!bMO "!b , M `H!b M q P x{ lMO L "!# Lh jb `b`#M0 q, jb `#hN !*!b LM lML`*iNM i w M0 MLj# h `# s &] !# j# L MOjb , lML~ !k x Mez"i M ~< M lMc!b L jbhN Lz"i MO N L M0 L M0~< jb lM `b lMc!kMs 8] < M y l `*!bMO "!b A i v jbhN `* `*!bM M M lM L lM hN {( jbhN aj# l`* "!# T &i Mc!*!bj# !# MO L l < f "!# dqPs { M lMOjb , B`#h MO N{ ` {NhN jb jk`* e M j#h e MO F 0 L "!# e i 7`* `*!bM Me MO ML L lMeMez"i i F`* j# eMs o 7 o 7 Y,Z [ &] 7 jbhN A`* |`H!kM Mf M lMf L lMBz"i M f lMf L lMfw MBjbM i "!# e lMB`#i Me i w MAMfjb h `# z"i 7 L L "!# !bi !*!kMe y jb lMdh O!b M M i di lMc!kM M lM0 L ML`# ; !#jkM `* jb LMO!bM T jb lM !# l ML j#h s12kd2=12mv2: M0~ !b L x i ; j#h 0~" M lMc!b z"i y v= (km)1=2d= 1:55ms: 8]_ j0 !b jb eMa A jb A~< ~ { v jbhN a`* jb eM z"i M n!bi !*!kM y j# Ma !b Mn M mo kw B xi i M M y j# M hN !# lMO lMO lM0 0 lM u(~< <~ j*!))}}}}}}

3 B !kMd A lM ~ j# 0 0h i !b f MO , j# Mc!#!#jb !b s12kd2= dmgs z"i s=kd22 dmg= 0:41m:RTS7U V<W Y Z [& ] ^ L O!b jb 0 !*!bj# l M ~ "!# 0hN !# M q rP PB MO MAi di Th `*!# MO !b jb T i jb h "!# !b jb L MO L "!# L l`* MO!# xj# Lh !# i ~ i L 0 ; M z"i Mx qJ s < M `b`#i eMA kw L Q P< lMAh O!b Mx jb MO!bMA MO L !# jb !bj# i l`b M0M0`b M MOjb , y M z"i Ms N &] Fz iNMO "!# LMOi L !kM0 j# M0 "!# jb M0 y M z"i ML h e h eM ~ jvM MO!# 0 0 !# j# hN j i T L <i !b " N 8] z"i MO "!# eM i L "!bM0 lMd!b Lh jkMc!#i jbML y M z"i M0`* ;`#i e MO jb `*h L qI M m tu* o 7 o 7 Y,Z [| N &] Ai x "!# j#~cMO L !# 0h e ;i T L "i !# nm !q P`bu( ; L O!b jb j# Mdi ; j# M0h M j# ;M E=P t= 3 104J: Q P" 8z"i `*!bMA j# MA~< eM `b`* j# !kMA M y M z"i MA`* !*!b A j# eMx 8 MO jb qJs 104 s Mc!b T kw 0 ~ i 0 M z"i MBj# eMO 0 "`H!kMO "!# { y M z"i MB 0h 0 L`*i `b 0 M ~ jb s MA~cMOjb M d | MO jb `# 7!#jkM `* jb LMe!)}

4 #i !#!bMx ~cM j# lMO ; j# M !b jb M Q= U= 2:7 104J: N 8] MO M L "!# e !b LhN jbMO!#i jkML y M z"i M0 Mc!b L M Q=mc T qJ 103 s ML i y T= Qmc= 3:22K:Y Z [( ] ^ Mx eM `b`#MApqI P x 7 TMf!b LhN jbMO!#i jkMf lMO 0 iqPo ~< jb l`# MO l Mc!kMBMA~ i L L `*!bM "!# `# xMjkM h h M j# L lMTh jb `b`* s `* l jbM T n L ei "M ` l MO e 0 MO!# 0 l ( eM `b`#Mx L lMOjb e q, sP J { MO l M j# &] lM ~ j# d oMc!#!# f M M ` { 8] lM ~cM j# lMO ; j# M !b jb ML M ` { 8] lMLz iNMO "!# !b L MO jb M `#`# jb !bM MO ; "M `s o 7 o 7 Y,Z [7 &] M ~ jb d <i Lh jk kw ~ i L "M `v x MO MsL= 0: 8]_ ; <i L jb L ; L ; L n=Mm= 2:49: ~ i L n `*!bMO "!b `* M h jb `b`# jbM h h lM {vhN jB y z"i MO n `H!kMc!# } G "M `eh j# !#!# y{ jkM h h lM MO kw n M!b Lh jkMc!#i jbMs i T=Ti= 273:2K: jb N U=32nR T= 8480J: 8] MO h jb 0 Lh jb h f M !b jb 0 M 0 l ML`# w M Q=L+ U= 8480J:JqPRr i jkMI | i jbM h jb eMrRTS7U V<W Y Z [F N]_^ NMd M j# l M !))}}}}

5 *!bj# l M `*!#jb i !bM i j# L L !b G`#ifi fh lMO 0 !b d`# O!*!b {<MOh h j# "`#`# LM M Li fh lMO !b s^ NMd M j# l M !*!bj# l Mdh i "!# jb L zq sI 10 15 ,hN "`H!kMdM `*!bM M qI D MO lMd`#i hN j* , h M { "!kMO MO & jk s MO LhN !#!#jb `*!bMO!# l `* M <i lMa i h i "!# Ma l `*!bMO M jqPsr MO M M j# l MazN{( jb ;h M m ~ i jbMIus &] !# j# L MOjb , ;~cMO jb lM0 `# !k L`*i h j# N M MOjb Ms o 7 o 7 Y,Z [ &] 7 MO Lh B !#!#jb `*!bMO!# l f 0 MO!# x MO MA`* L LM m ~ !*!b jb M u 7 MO LhN x !#!#jb `*!bMO!# l B Fh M B Lz"i Me MOjb Ms M 0h L jkMc!b 0 M h lMO L j#!# MO ,M h M e`H!b `b`* 0 xi i MO T L i eM Epiano= 2"0; L !bj# z"i L jkMc!b 0 M lM0 MOjb l Mxm i `b !b jbM lMO 0 "!# MO ML MOjb M `*!# `#`bM u( i i MO x L < i fM Eq=q4 "0r2: i 8`* e~ lMO L T kw L 8 i f MO Lh (`* M <i n`*i h M n ~ L `b`* j# e l`*!#jb i !kMAi M M j# l MAhN "`* !# ~cMT L B kw 7 MO Lh f !#!#jb f`* lMLi `b !b d ML `#`# s L < i A`* ~ M ~ jb kw F M LhN B h M e di i M Mez"i e lM0 MOjb M Epiano=Eq!)))}}}

6 2"0=q4 "0r2: i =q2 r2= 2 10 11C=m3:Y Z [e ] ^ NM MOjb M l`*!#jb i !kM i j# L 0 "!# `*i i M `* jkM jkMO qI P s^ M M j# l M !*!bj# l Mh i "!# jb 0 zqG > 10 12 hN "`H!kM0ML l `*!bMO M0jqI MO ; "!#jb e lM0`* jkMs N &] !# j# L MOjb F~cMO jb `* F MO Lh e !*!bj# "`H!kMc!b e Fh i "!# { `*!bM "!# q r M jk f lMe`H jbM ;h T~< Lh `b`* M lML MOjb l M0ze <i m ~ N i jkMJus o 7 o 7 Y,Z [| PqdRO i jkMJ | i jbM h jb eM N M 0h L h i "!# m !b jb LMO ML`* jkM u8 Mc!# e M lM0`* 0 eMTm ~ !#!# jb lMO u( ; MO Lh ; lML MOjb l Mdzf M`* jkMs i 0 M 0h w MO e MB`H!b `b`#Me jb hN j,M <i lMOjk`# ~ fM ~ jb ~ jk`# ; h h `*!# y Me MOjb M ~ z"i `b`* j# h `# !b ~cMs MO Lh L Me MOjb M ze ~ M Eq=q4 "0(R r d)2: F MO Lh e Me`* jkM ;h i "!# {N kw `# O!*!b A lML KMOi `b`v Esf era=Q(R d)4 "0R3:^ i M M 0 0 i f ; i MO Lh `# ;w M Q= qR3(R r d)2(R d)= 1:0 10 10C:RTS7U V<W Y Z [( N] , jb MO MO!# Li M ~<~ 0 "!))}}

7 # L N= 900`*h jb d A jkMO L fmo Fjb `# `*!# M0!bjbM `# i jkMO u M ~"~ !# Tjb M j# !b Mc!#!# jb LM Ai jb e x lMO L !#jb d= 10 D i l= 20 s &] Tz"i MO MOh h jb `# l`* eMO G h `b`* MO l M j# , N i !*!kMO M 8] i M ~cMO jb emoM h h jb `b`* eMc!# <u8 N i !*!kMO M N 8] < L y i !*!bM Mx~< e "Mc!kMBMO y M L "!bM L jb !# mV = 220{f= 50 u {Fz"i M e jbj# !b d e M MO!*!bjbM ~ jk`* jb lML M ] < lMajb `# l`H!b ~< !b GjbM 0 T = 1:68 10 9 T{( lM i w M & f= 283 x{( G lMO L !bj# & s= 1 L T{ z"i MO `#M jb lMLj# `* l`H!b M !b O!kMO M0 M o 7 o 7 Y,Z [ i `bM y MOh h jb `b`# eMO , `# N !kML i w M 8] ^`bMO N L M jb di ML ;`* l Ll= 0 Nl 2 M j# M { h `b`* lMO L e`# j# ~ j# L= 0N2l d2 2= 0:0400 N 8]_ }h j# `* Mn 8!b `# B`# <i `# l M {| != 2 f{7 Ai `bMO Vp iph j (~cMO jb ( v 8!b `# f jbj# "!# ;h l {V(t) =Ldi(t)dt;Vpsin(!t+ ) =Lddt(ipsin!t) =L!ipcos!t; ^`#M L j# M !#jkM0~cMO jb ; h l e ~cMO jb f M h j `# MO ;`# <i `# l MO y{Vp=p2V ;ip=p2i ;i =1p2p2V !))))}}}}}}}}}

8 L;i =V !L= 17:5193 ]R= f (s=2)2= 0:6053 Y Z [F ] ^ B `#MO!# j# C= 700 ~< MOjb l Mc!b Md fi NM !b `# V= 44 d{< ,hN `b M j# l MO!# MO N dMO `#i M h i M0jb `# `*!# M0 MR= 10 s N &] xz"i M "!# 0!# 0h e lMd!b `# MO F`*i ; M h h M `b`bM !bjbM2=3 1=3 V= 44 o 7 o 7 Y,Z [| N N`#MO!# jb `* ;`b M j# l M0`* L M0 jkMOjb MV(t) =Vexp tRC {23V=Vexp t1RC ;t1= RClog23;t2= RClog13; t=t2 t1= RC log13 log23 =RClog2 = 4:8520 e`r}}