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%OwW|t s=Hv=� = md

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f = !s

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CqO=at 'u}=Q@=v@ "OQ=O l}UqmQ}e |}=Q}t QwmPt |xv=t=U '4 |x]@=Q T=U= Q@"Ow@ Oy=wNv Q}PBu=mt= =yv; |R=U=OH w xOW Q}oQO Qo}Om} =@ |}=Q}t |xr}Uw x@ |OwtpL |=yVwQ R= O}=@ w OQw; CUOx@ |Owt p}rLD =@ =Q xR=U |}=Hx@=H u=wD|tv TB|=y|oS} w '|OOa |=yOv}=Qi R= xO=iDU= =@ 'Q[=L Q=DWwv QO "OQm xO=iDU= |OOau} wv |Ov}=Qi 'Q=my=Q u}= "Ov=xOt; CUOx@ =Q}t |xR=U |=Q@ |tQH Qo =Q}t |xv}y@

"Ow@ Oy=wN 'OvQ=O |}=Q}t xm '|ak=w |=yxR=U |tQH Qo =Q}t |L=Q] QO

xOWKqY= lQ=tw}v VwQ "3wO |xv=t=U |}=Q}t uOw@ l}UqmQ}e p}rO x@ 'xOW xQ=W= QDV}B xm xvwo u=ty|OOa pL |=yVwQ R= O}=@ w CU}v umtt |Owt p}rLD R= xO=iDU= '|O=R; xHQO|irDNt |=yVwQ |OOa CQwYx@ =yxR=U MU=B uOQw; CUOx@ |=Q@ "OwW xO=iDU=OwW|t ZQi u; QO xm 'CU= xOW xO=iDU= lQ=tw}v VwQ R= =Hv}= QO xm OQ=O OwHw|x_Lr QO |rw 'OvW=@ swrat ti |x_Lr QO xR=U ?=DW w 'CaQU '|}=Hx@=H|x_Lr R= =Q xR=U |}=Hx@=H O}=@ 'TB "OvDU}v XNWt =yMU=B R= s=Om I}y ti+16 |x]@=Q CQwYx@ |v=tR s=o 'Q=mu}= |=Q@ "OQw; CUOx@ Q_v OQwt u=tR =D CUNv

%OwW|t h} QaD� t = ti+1 � ti (6)

CmQL CqO=at s}kDUt pL |=Q@ w xYqN CQwYx@ lQ=tw}v VwQ '1 pwOH QO|x_Lr QO hrDNt |=yC}tm Q=Okt uO=Ou=Wv |=Q@ 0 T} wvQ} R 'u; QO w xOW x�=Q=

[23]"lQ=tw}v VwQ "1 pwOH%x}rw= C=@U=Lt "1

M �U0 = P0 �C _U0 �KU0 ) �U0 uOQm pL "1"1�t ?=NDv= "2"1K = K +

��tC + 1�(�t)2M "3"1

a = 1��tM +

�C; "4"1b = 1

2�M + �t( 2� � 1)C

%i |v=tR s=o Qy |=Q@ C=@U=Lt "2�P i = �P i + a _U i + b �U i "1"2K�U i = �P i ) �U i uOQm pL "2"2� _U i =

��t�U i � �

_U i + �t(1� 2� ) �U i "3"2

� �U i = 1�(�t)2 �U i � 1

��t_U i � 1

2� �U i "4"2U i+1 = U i + �U i; _U i+1 = _U i + � _U i; "5"2�U i+1 = �U i + � �U i

1�2 pL=Qt uOQ@ Q=mx@ w i+ 1 =@ i |Q=Po|=H%|Oa@ |v=tR s=o |=Q@ Q=QmD "3"|Oa@ |v=tR 5�2 =D

37

"""|tQH

Qo=Q}t|

xv}y@C

=YNWt

u}}aD

"xOWKqY= lQ=tw}v VwQ "2 pwOH%x}rw= C=@U=Lt "1

M 0 �D0 = P 00 � 2�C0 _D0 �K0D0 ) �D0 uOQm pL "1�1�t! ?=NDv= "2�1K = K0 + 2�

��t!C0 + 1

�(�t!)2M 0 "3"1a = 1

2���t!M0 +

�C0; "4"1

b = 12�M 0 + 2��t!( 2� � 1)C0

%i |v=tR s=o Qy |=Q@ C=@U=Lt "2�Pi = �P 0i + a _Di + b �Di "1"2K�Di = �P i ) �Di uOQm pL "2"2� _Di =

��t!�Di �

�_Di + �t!(1�

2� ) �Di "3"2� �Di = 1

�(�t!)2 �Di � 1��t!

_Di � 12� �Di "4"2

Di+1 = Di + �Di; _Di+1 = _Di + � _Di; "5"2�Di+1 = �Di + � �Di

=D 1�2 pL=Qt uOQ@ Q=mx@ w i+ 1 =@ i |Q=Po|=H%|Oa@ |v=tR s=o |=Q@ Q=QmD "3"|Oa@ |v=tR 5�2

xv}y@ Q}O=kt uOQw; CUOx@ "4� w � 'fd 'f XNWt Q}O=kt |=Q@ (D) xR=U |}=Hx@=H C@Uv '3 VN@ QOu}ov=}t |R=Uxv}tm 'fd |xv}y@ Q=Okt u}}aD |=Q@ "CU= xOt; CUOx@ t! ?ULQ@xO} RoQ@ |tQH Qo =Q}t |R=Uxv}y@ Q=}at u=wvax@ xR=U |}=Hx@=H C@Uv jr]tQOk`@=D |=Q@ =Q u}ov=}t u} QDtm xm |Q=Okt 'fd hrDNt Q}O=kt u=}t R= 'u}=Q@=v@ "OwW|t"OwW|t ?=NDv= xv}y@ Q=Okt u=wvax@ 'Ovm x�=Q= u}at |v=tR |xR=@ l} QO ' jDjQ=Owtv 'OwW |UQQ@ ,qt=m Q_vOQwt l}vwtQ=y l} QLD QF= QO xR=U Q=DiQ xmv}= |=Q@=@ u=wD|t =Q t!e pt=a "OwW|t sUQ 0 � t! � t!e |xR=@ QO xOt; CUOx@ `@=D19 |x]@=Q QO t |=H x@ u}tR =} xR=U ?w=vD |xQwO |xv}W}@ Q@=Q@ 5 |Q=Po|=H

%OQw; CUOx@ 27 |x]@=Q j@=]tt!e = max

�5!s Ts = 10�; 5! s T = 10�

f

�(27)

lJwm R= u=v}t]= |=Q@ "OyO|t u=Wv =Q u}tR CmQL ?w=vD |xQwO T 'u; QO xm|x]@=Q pmW x@ �t! '12 w 10 \@=wQ x@ xHwD =@ w xrLQt Qy QO |v=tR s=o uOw@

%OwW|t xDiQo Q_v QO 28�t! = min

�15 (0 389!s TJ) = 0 0778 !s TJ ; 0 001

�(28)

&O@=}|t Vy=m |tQH Qo =Q}t |DNU 'fd V}=Ri= =@ xm OyO|t u=Wv 15 |x]@=Qu}ty x@ "OW Oy=wN QiY ,=@} QkD Qo =Q}t |DNU 'u; nQR@ Q=}U@ |=yQ=Okt |=Q@ TB|xar=]t "OQ}o|t Q=Qk |UQQ@ OQwt 0 < fd � 5 <=R= x@ \ki xR=U Q=DiQ 'p}rO'T=U= u}= Q@ "OwW|t s=Hv= |OOa CQwYx@ fdhrDNt |=yQ=Okt |=Q@ xR=U Q=DiQQO fd hrDNt |=yQ=Okt |=Q@ jDj Q=Owtv '� w � 'f XNWt Q=Okt |=Q@ CUNvxDW=O =Q u}ov=}t u} QDtm xm |Q=Okt 'TBU "OwW|t sUQ 0 � t! � t!e |xR=@jr]tQOk `@=D xm CU= uWwQ "OwW|t xO} RoQ@ xv}y@ Ot=U@ C@Uv u=wvax@ 'OW=@R}v =Q |vLvt Q} R sHL u} QDtm 'xv}y@ Q}O=kt <=R= x@ (jDj) xR=U |}=Hx@=H C@Uv

"CW=O Oy=wN t! |=Q@ xOWxDiQo Q_v QO |xR=@ QO

!d =pkd=md w!s =

pk=m ?}DQD x@ 'OvwW ZQi Qo}Om} R= =OH xm

k 'm Q@ ?}DQDx@ xv=t=U |}=Q}t w '|DNU 'sQH |=yT} QD=t 'TBU "Ow@ Ovy=wN%�18 |r= 16 \@=wQ� OvwW|t s}UkD c w

M 0 =

"1 00 �

#(16)

K0 =

241 + f2f2d� � f2

f2d�

� f2f2d� f2

f2d�

35 (17)

C0 =

"1 00 0

#(18)

%OwW|t h} QaD 19 |x]@=Q CQwYx@ t! C}tmt! = !s t = 2� t

Ts(19)

MU=B |xvt=O 'u}vJty "OyO|t u=Wv =Q |rY= |xR=U ?w=vD |xQwO Ts 'u; QO xm%OwW|t xDiQo Q_v QO 20 |x]@=Q CQwYx@ xR=U |m}D=DU=

ust0 = mak

(20)

C@Uv xR=U |}=Hx@=H lQ=tw}v VwQ QO 'CU= xOW xQ=W= u}= R= V}B xm xvwo u=ty|}=Hx@=H |xvt=O x@ xR=U |}=Hx@=H C@Uv 'VN@ u}= QO "O};|t CUOx@ u=tR x@j@=]t� =yC}tm u}=h} QaD =@ Q=m u}= "CU= xOt;CUOx@ t! ?UL Q@ u; |m}D=DU=

%OwW|t R=e; �23 |r= 21 \@=wQ

D =

(D

Dd

)= 1ust0

U (21)

_D = !sa

_U (22)

�D = 1a

�U (23)

|=Q@ "Ov}; CUOx@ Oa)@|@ CQwYx@ O}=@ 1 pwOH QO xOW|iQat |=yC}tm'K |=yC}tm 'TBU "OwW|t s}UkD ma Q@ 1 pwOH R= 1�1 s=o 'Q=mu}=QO xm wQ}v Q=OQ@ 'u}vJty "OvwW|t s}UkD m w c 'k Q@ ?}DQDx@ b w aKqY= 24 |x]@=Q pmW x@ 'ma Q@ s}UkD =@ 'CU= xOW xO=O u=Wv 7 |x]@=Q

%OwW|t

P 0i = �M 0Ia

�ugi (24)

25 |x]@=Q j@=]t u=wD|t 1 |x]@=Q x@ xHwD =@ =Q u}tR ?=DW �ugi 'u; QO xm%CWwv

�ugi = a sin(ti) = a sin(f t!i) (25)

�t! =@ �t C}tm u; QO xm 'OyO|t u=Wv =Q xOWKqY= lQ=tw}v VwQ '2 pwOH|x]@=Q R= xm OyO|t u=Wv =Q xR=U |}=Q}t C@Uv � 'u}vJty "CU= xOW u} Ro}=H

%O};|t CUOx@ 26� = c

2m!s= c

2pkm (26)

38

2 2|xQ

=tW'33

�2|xQ

wO'�13

96u=DU

@=D�h}

QWu=Qt

a|UOv

yt "� = 0 |=Q@ fd Q}O=kt "3 pwOH

0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 16 1 15 1 14 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 15 1 15 1 14 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 13 1 13 1 13 1 13 1 12 0 21 16 1 15 1 15 1 14 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 0 31 15 1 15 1 14 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 12 0 41 16 1 16 1 15 1 15 1 14 1 14 1 14 1 13 1 13 1 13 1 12 1 13 1 12 1 12 1 12 0 51 14 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 12 0 61 13 1 13 1 13 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 11 1 10 1 10 1 09 1 07 0 71 12 1 11 1 11 1 11 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 09 1 09 0 81 10 1 10 1 10 1 09 1 08 1 08 1 07 1 06 1 05 1 04 1 04 1 03 1 02 1 01 1 00 0 91 08 1 07 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 04 1 03 1 03 1 02 1 01 1 00 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 03 1 04 1 11 07 1 07 1 06 1 04 1 03 1 02 1 01 1 00 0 99 0 98 0 97 0 98 1 01 1 03 1 04 1 21 03 1 03 1 03 1 03 1 03 1 04 1 03 1 03 1 03 1 02 1 00 0 99 1 37 1 36 1 34 1 31 04 1 03 1 02 1 02 1 01 1 00 0 99 0 98 0 98 0 98 0 98 1 37 1 36 1 34 1 33 1 41 03 1 03 1 03 1 03 1 39 1 37 1 04 1 69 1 67 1 65 1 64 1 62 1 60 1 56 1 54 1 51 88 1 84 1 78 1 72 1 68 1 67 1 68 1 68 1 52 1 52 1 53 1 54 1 55 1 56 1 55 1 61 73 1 71 1 68 1 64 1 60 1 60 1 59 2 00 1 94 1 91 1 89 1 87 1 72 1 75 1 74 1 72 04 2 01 1 93 1 93 1 92 1 91 1 91 1 76 1 67 1 77 1 78 1 78 1 79 1 78 1 77 1 82 18 1 94 1 90 1 83 1 83 1 83 1 83 2 14 2 14 2 12 1 90 1 91 1 92 1 93 1 94 1 92 31 2 08 2 08 2 08 2 08 2 06 2 05 2 04 2 03 2 03 2 03 2 02 2 02 2 00 1 98 2 02 32 2 31 2 31 2 04 2 03 2 03 2 28 2 19 2 19 2 19 2 18 2 17 2 14 2 14 2 13 2 12 54 2 50 2 47 2 45 2 45 2 44 2 22 2 21 2 22 2 27 2 27 2 27 2 25 2 21 2 19 2 22 60 2 59 2 38 2 32 2 31 2 54 2 52 2 51 2 50 2 49 2 32 2 32 2 33 2 34 2 33 2 32 79 2 76 2 70 2 68 2 67 2 51 2 50 2 52 2 53 2 53 2 52 2 41 2 43 2 43 2 39 2 43 07 2 57 2 57 2 57 2 57 2 57 2 70 2 70 2 69 2 68 2 66 2 63 2 53 2 53 2 54 2 5

=vU}@ w |Dr} R |=yx]@=Q =@ |O=yvW}B Q}O=kt VHvU "5u}@ |}xU}=kt 'Q[=L Q=DWwv QO xOWO=yvW}B Q}O=kt |}=Q=m |@=} RQ= |=Q@ 'xt=O= QO[5]'Vv=Q=mty w |Dr} R "CU= xOW s=Hv= Qo}O |tQH |=yQo =Q}t w |O=yvW}B Qo =Q}txOW?PH |SQv= uOQm xv}W}@ w |rY= |xR=U |W@vH |SQv= |R=Uxv}tm Q=}at=Q 30 w 29 |=yx]@=Q w ?=NDv= |R=Uxv}y@ Q=}at u=wvax@ =Q |tQH Qo =Q}t \UwD

x@ w � = 7 =D � = 0 |=Q@ =Q fd |xv}y@ Q}O=kt '10 |r= 3 |=ypwOHxHwD O}=@ "OvyO|t u=Wv xR=U hrDNt |=yOt=U@ C@Uv w =ysQH C@Uv <=R=[21]'Ci=} =Q xv}y@ Q}O=kt R}v |Owt p}rLD R= u=wD|t '� = 0 |=Q@ xm CW=OOvy=wN u=Um} 3 pwOH Q}O=kt =@ R}v QwmPt VwQ =@ xOt; CUOx@ G}=Dv xm

"Ow@

39

"""|tQH

Qo=Q}t|

xv}y@C

=YNWt

u}}aD"� = 0=01 |=Q@ fd Q}O=kt "4 pwOH

0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 0 21 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 31 15 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 15 1 14 1 14 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 51 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 0 61 14 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 10 1 10 1 10 1 09 1 08 0 71 13 1 12 1 11 1 11 1 11 1 11 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 08 1 08 0 81 10 1 10 1 10 1 09 1 09 1 08 1 07 1 06 1 06 1 05 1 04 1 03 1 02 1 01 1 01 0 91 08 1 08 1 07 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 03 1 03 1 02 1 01 1 01 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 03 1 03 1 11 07 1 07 1 06 1 04 1 03 1 02 1 01 1 00 0 99 0 98 0 97 0 97 0 98 0 99 1 01 1 21 03 1 03 1 03 1 03 1 03 1 04 1 03 1 02 1 02 1 01 1 00 0 99 1 40 1 37 1 35 1 31 04 1 03 1 02 1 02 1 01 1 00 0 99 0 98 0 98 0 98 0 98 0 96 1 35 1 34 1 32 1 41 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 68 1 65 1 64 1 62 1 60 1 57 1 55 1 51 91 1 89 1 86 1 84 1 69 1 68 1 67 1 67 0 97 1 52 1 53 1 54 1 55 1 56 1 55 1 61 73 1 71 1 68 1 64 1 61 1 60 1 58 2 00 1 98 1 92 1 89 1 87 1 84 1 77 1 75 1 72 05 2 02 1 93 1 92 1 92 1 91 1 91 1 90 1 67 1 68 1 78 1 78 1 78 1 78 1 76 1 82 18 2 17 1 81 1 82 1 82 1 82 1 83 2 15 2 14 2 13 2 12 2 10 1 92 1 95 1 95 1 92 44 2 45 2 44 2 44 2 08 2 06 2 05 2 04 2 03 2 03 2 03 2 02 2 02 2 00 1 98 2 02 47 2 31 2 31 2 02 2 03 2 03 2 28 2 27 2 26 2 19 2 18 2 17 2 14 2 15 2 15 2 12 55 2 51 2 47 2 45 2 44 2 44 2 43 2 21 2 23 2 27 2 27 2 27 2 25 2 21 2 18 2 22 86 2 85 2 84 2 32 2 31 2 54 2 52 2 51 2 50 2 49 2 48 2 46 2 33 2 35 2 35 2 32 80 2 77 2 70 2 68 2 68 2 67 2 66 2 52 2 53 2 53 2 52 2 51 2 46 2 43 2 39 2 43 11 3 10 2 57 2 57 2 57 2 57 2 70 2 70 2 81 2 80 2 67 2 66 2 53 2 54 2 55 2 5

%Ow@ Ovy=wN 34 w 33 \@=wQ CQwYx@ ?}DQD x@fdZ = f

p1 + � (33)

fdB = f(1 + �) (34)

Cr=L 3 |=Q@ 'u; |m}D=DU= |}=Hx@=H |xvt=O x@ xR=U |}=Hx@=H C@Uv jr]tQOk'Q[=L Q=DWwv QO xOWO=yvW}B |tQH Qo =Q}t x@ pYDt |xR=U |=Q@ |va} 'Q_vOQwt%�37 |r= 35 \@=wQ� Ov=xOW xO=O u=WvRB wRZ 'Rp =@ ?}DQD x@ =vU}@ w '|Dr} RRp =

����Djfd = fdp

���� (35)

RZ =����Djfd = fdZ ; �d = �dZ

���� (36)

RB =����Djfd = fdB ; �d = �dB

���� (37)

|O=yvW}B |tQH Qo =Q}t |xv}y@ Q}O=kt |xOvyOu=Wv fdp C}tm '35 |x]@=Q QO'Rp |=ypt=a u=wD|t '?}DQD u}O@ "Ov=xOW x�=Q= 10 |r= 3 |=ypwOH QO xm CU=

"OQw; CUOx@ t! w � w � 'f ?ULQ@ =Q RB w RZQ=Okt |=Q@ QwmPt C}tm 3 Q=Owtv CUNv 'Q_vOQwt |=yQo =Q}t OQmrta |UQQ@ |=Q@

%Ov=xOQm O=yvW}B |tQH Qo =Q}t |}=Q}t w |DNU |=Q@kdZ = mdk

m+md(29)

�dZ = 12rmd

m(30)

Ov=xOQm x�=Q= |tQH Qo =Q}t |L=Q] |=Q@ =Q |WwQ [20]'wUwQ=m w =vU}@ 'Qo}O |wU R=MU=B Vy=m CaQU |R=Uxv}W}@ =@ w xDiQo Q_v QO =Q xR=U |=QPo MU=B u; QO xmC@Uv |OQ@ Q=m Q}O=kt |=Q@ =Q |tQH Qo =Q}t |xv}y@ |=y|oS} w 'u=tR x@ C@Uv =QPo

%Ov=xOQw; CUOx@ 32 w 31 \@=wQ CQwYx@ sQH

kdB = mmdk(m+md)2 (31)

�dB =r

md

m+md(32)

x@ xHwD =@ [4]"CU= xOQm O=yvW}B =Q 31 |x]@=Q �2011� =Ov=Q}t 'QDV}B u}vJty=vU}@ w |Dr} R |tQH Qo =Q}t Ot=U@ x@ u}tR CmQL Ot=U@ C@Uv '31 w 29 \@=wQ

40

2 2|xQ

=tW'33

�2|xQ

wO'�13

96u=DU

@=D�h}

QWu=Qt

a|UOv

yt "� = 0=02 |=Q@ fd Q}O=kt "5 pwOH

0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 21 15 1 15 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 31 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 14 1 14 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 51 15 1 15 1 14 1 13 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 1 10 0 61 14 1 13 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 10 1 10 1 09 1 09 1 09 0 71 13 1 13 1 12 1 11 1 11 1 11 1 11 1 10 1 10 1 10 1 10 1 10 1 09 1 08 1 08 0 81 10 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 06 1 05 1 05 1 04 1 03 1 02 1 01 0 91 08 1 08 1 07 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 03 1 03 1 02 1 02 1 01 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 03 1 03 1 11 07 1 07 1 06 1 04 1 03 1 02 1 01 1 00 0 99 0 98 0 97 0 98 0 97 0 99 0 99 1 21 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 01 1 00 0 99 0 98 1 38 1 36 1 31 04 1 03 1 02 1 02 1 01 1 00 0 99 0 99 0 98 0 99 0 98 0 97 0 97 1 33 1 32 1 41 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 00 0 99 1 64 1 63 1 61 1 58 1 56 1 51 03 1 03 1 02 1 02 1 01 1 01 1 00 0 99 0 97 0 97 0 98 0 99 1 55 1 55 1 54 1 61 04 1 04 1 03 1 63 1 61 1 60 2 03 2 01 1 98 1 94 1 89 1 87 1 84 1 79 1 76 1 72 08 1 94 1 93 1 93 1 92 1 92 1 92 1 92 1 68 1 68 1 77 1 78 1 78 1 77 1 76 1 82 80 2 77 1 82 1 82 1 82 1 83 2 15 2 14 2 14 2 13 2 12 2 11 2 08 1 96 1 96 1 92 41 2 43 2 43 2 44 2 43 2 41 2 40 2 38 2 04 2 03 2 03 2 02 2 02 1 99 1 97 2 02 51 2 71 2 71 2 30 2 85 2 83 2 81 2 78 2 58 2 53 2 19 2 18 2 14 2 16 2 16 2 12 59 2 53 2 49 2 46 2 45 2 64 2 62 2 61 2 22 2 26 2 27 2 27 2 25 2 21 2 18 2 22 87 2 85 2 84 2 83 2 82 2 82 2 53 2 51 2 51 2 64 2 64 2 47 2 42 2 36 2 36 2 32 81 2 76 2 69 2 69 2 68 2 68 2 83 2 85 2 82 2 53 2 52 2 51 2 48 2 43 2 39 2 43 21 3 21 3 22 3 22 3 21 3 20 3 20 2 71 2 81 2 80 2 78 2 75 2 54 2 55 2 56 2 5

"� = 0 05 w � = 0 05 |=Q@ Rp Q=Owtv "2 pmW

C@Uv Q}O=kt s=tD <=R= x@ =yv; |@=} RQ= |=Q@ 'TBU &CU= xOW sUQ � w �XNWt"CU= xOW |iQat |O}OH |=yC}tm 'sQH

� = 0 05 <=R= x@ RB w RZ 'Rp |=yQ=Owtv ?}DQD x@ '4 |r= 2 |=ypmW QOxO=O u=Wv 0 � t! � 20 w 0 < f � 2=5 |xOwOLt QO � = 0 05 wCr=L QO |O=yvW}B |tQH Qo =Q}t xm OUQ|t Q_v x@ =yu; x@ xHwD =@ xm 'Ov=xOWR= xR=U MU=B Vy=m QO |QDW}@ |}=v=wD 'u=tR CWPo =@ xS} w x@ w (f = 1) O}OWD0 < f < 2=5 |xOwOLt w u}at |=ysQH C@Uv |=Q@ 'uwvm = "OyO u=Wv OwNxU}=kt =vU}@ w |Dr} R |=yx]@=Q =@ |O=yvW}B |=yQ=Okt ' 0 � t! � t!e wC}tm 'Q=mu}= s=Hv= |=Q@ "CU= xOW h} QaD 27 |x]@=Q QO t!e C}tm "CU= xOWx@ 'OW=@ RZ R= QDnQR@ Rp =yv; QO xm |}=yCtUk CL=Ut C@Uv u=wvax@ AZ

41

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0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 0 21 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 31 15 1 15 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 0 51 15 1 14 1 14 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 1 11 1 10 1 10 0 61 14 1 13 1 13 1 12 1 12 1 11 1 11 1 11 1 10 1 10 1 10 1 09 1 09 1 09 1 09 0 71 13 1 13 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 10 1 10 1 09 1 09 1 08 1 07 0 81 11 1 10 1 10 1 10 1 09 1 08 1 08 1 07 1 07 1 06 1 05 1 04 1 03 1 02 1 01 0 91 08 1 08 1 07 1 07 1 07 1 06 1 05 1 05 1 04 1 04 1 04 1 03 1 02 1 02 1 01 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 03 1 02 1 02 1 02 1 03 1 11 06 1 06 1 06 1 04 1 03 1 02 1 01 1 00 0 99 0 98 0 98 0 98 0 97 0 98 0 99 1 21 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 01 1 00 0 99 0 98 0 97 1 37 1 31 04 1 03 1 03 1 02 1 01 1 00 0 99 0 99 0 99 0 99 0 98 0 97 0 98 0 98 1 31 1 41 04 1 03 1 03 1 03 1 03 1 03 1 03 1 01 1 00 0 99 0 99 0 98 1 61 1 59 1 57 1 51 03 1 03 1 02 1 02 1 02 1 01 1 00 0 99 0 98 0 98 0 98 0 98 0 98 1 54 1 53 1 61 04 1 04 1 03 1 03 1 03 1 03 1 02 1 01 1 00 1 94 1 89 1 86 1 84 1 80 1 77 1 71 04 1 04 1 04 1 03 1 02 1 01 1 00 0 99 0 99 0 99 0 98 1 77 1 77 1 77 1 75 1 82 78 2 76 2 74 2 71 2 68 2 64 2 61 2 14 2 13 2 13 2 11 2 10 2 07 1 99 1 97 1 92 42 2 43 2 44 2 45 2 43 2 42 2 40 2 39 2 37 2 03 2 02 2 02 2 01 1 99 1 97 2 03 10 3 07 3 03 2 84 2 85 2 84 2 84 2 82 2 81 2 54 2 37 2 36 2 15 2 18 2 17 2 12 69 2 69 2 68 2 68 2 67 2 66 2 65 2 64 2 63 2 61 2 27 2 27 2 25 2 20 2 17 2 23 45 2 89 2 85 2 83 2 82 2 82 2 82 2 79 2 52 2 68 2 63 2 50 2 45 2 38 2 37 2 32 82 2 71 2 69 2 69 2 69 2 77 2 82 2 84 2 84 2 83 2 53 2 50 2 48 2 43 2 38 2 43 24 3 23 3 23 3 24 3 23 3 23 3 23 3 22 3 26 2 80 2 79 2 75 2 72 2 57 2 57 2 5

C@Uv 'u}vJty "CU= xOW |iQat 'CU=Rp R= QDnQR@RZ =yu; QO xm |}=yVN@|}=yCtUk CL=Ut x@ 'OW=@ RB R= QDnQR@ Rp =yv; QO xm |}=yVN@ CL=Ut

%OwW|t xO=O u=Wv AB O=tv =@ 'CU= Rp R= QDnQR@ RB =yv; QO xmAZ = f0 < f � 2 5; 0 � t! � t!e jRZ < Rpg

f0 < f � 2 5; 0 � t! � t!e jRZ > Rpg (38)

AB = f0 < f � 2 5; 0 � t! � t!e jRB < Rpgf0 < f � 2 5; 0 � t! � t!e jRB > Rpg (39)

|=yQ=Okt =yu; QO xm t! w f R= |}=yxOwOLt |@=} RQ= |=Q@ AB w AZ |=yC}tm'CU= uWwQ "OvwQ|t Q=m x@ 'OQ=O |QDQ@ =vU}@ w |Dr} R |=yx]@=Q Q@ |O=yvW}B|O=yvW}B |tQH Qo =Q}t OQmrta 'OvwW 1 R= QDtm AB w AZ |=yC}tm xJv=vJ|=yx]@=Q� =vU}@ Qo =Q}t w �30 w 29 |=yx]@=Q�|Dr} R Qo =Q}t R= �10 =D 1 |=ypwOH�

"CU= Q=QkQ@ R}v xDmv u}= Tma "CU= QDy@ �32 w 31sUQ � = 0 05 |=Q@ � x@ C@Uv AB w AZ |=yC}tm Q=Owtv '5 pmW QOp@=kt QO |O=yvW}B |DNU OQmrta |xOvyOu=Wv ?}DQD x@ C}tm wO u}= "Ov=xOWC}tm wO Qy 'CU= XNWt 5 pmW QO xmu=vJ "OvDUy =vU}@ w |Dr} R |=yQo =Q}tOyO|t u=Wv u}= "OvDUy 1 R= QDlJwm |tQH |=yC@Uv s=tD <=R= x@ AB w AZ\@=wQ R= V}@ Q_vOQwt |xR=@ |t=tD QO |O=yvW}B Q}O=kt uOw@xv}y@ p=tDL= xm

"� = 0 05 w � = 0 05 |=Q@ RZ Q=Owtv "3 pmW

"� = 0 05 w � = 0 05 |=Q@ RB Q=Owtv "4 pmW

42

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0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 0 21 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 31 16 1 15 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 14 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 0 51 15 1 14 1 14 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 1 10 1 10 1 10 0 61 14 1 13 1 13 1 12 1 12 1 11 1 11 1 10 1 10 1 10 1 10 1 09 1 09 1 09 1 09 0 71 13 1 13 1 13 1 13 1 12 1 12 1 11 1 11 1 11 1 10 1 09 1 09 1 08 1 08 1 07 0 81 11 1 11 1 10 1 10 1 09 1 09 1 08 1 07 1 07 1 06 1 06 1 05 1 04 1 03 1 02 0 91 08 1 08 1 08 1 07 1 07 1 07 1 06 1 05 1 05 1 04 1 04 1 03 1 03 1 02 1 01 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 02 1 02 1 03 1 11 06 1 06 1 05 1 04 1 03 1 02 1 01 1 00 0 99 0 99 0 98 0 98 0 98 0 98 0 99 1 21 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 01 1 00 0 99 0 98 0 97 0 97 1 31 04 1 03 1 03 1 02 1 01 1 01 0 99 0 99 0 99 0 99 0 98 0 98 0 98 0 98 0 97 1 41 04 1 03 1 03 1 03 1 03 1 03 1 03 1 01 1 00 0 99 0 99 0 98 0 98 1 60 1 58 1 51 03 1 03 1 03 1 02 1 02 1 01 1 00 0 99 0 99 0 99 0 99 0 98 0 98 0 98 1 53 1 61 04 1 04 1 04 1 03 1 03 1 03 1 02 1 01 1 00 0 99 0 99 1 86 1 84 1 81 1 78 1 71 04 1 04 1 04 1 03 1 02 1 01 1 00 1 00 1 00 0 99 0 99 0 99 1 77 1 76 1 74 1 81 05 1 05 1 04 2 72 1 02 1 01 1 00 1 00 1 00 1 00 2 11 2 10 2 07 2 01 1 98 1 92 44 2 46 2 47 2 45 2 43 1 01 1 01 1 01 1 00 1 00 0 99 2 01 2 00 1 98 1 96 2 03 10 3 09 3 06 3 00 2 90 2 89 2 87 2 86 2 85 2 84 2 43 2 37 2 31 2 21 2 19 2 12 68 2 68 2 69 2 70 2 70 2 70 2 70 1 01 2 81 2 80 2 77 2 27 2 23 2 19 2 17 2 23 41 3 40 3 39 3 38 3 37 3 35 3 31 3 26 3 21 2 68 2 61 2 55 2 53 2 40 2 39 2 33 26 2 71 2 69 2 69 2 70 2 72 3 20 2 84 2 83 2 83 2 83 2 48 2 47 2 42 2 38 2 43 22 3 22 3 23 3 23 3 23 3 23 3 23 3 23 3 22 3 21 2 79 2 78 2 77 2 60 2 59 2 5

|tQH Qo =Q}t OQmrta QO |v=OvJ Q}F-=D sQH C@Uv 'u}vJty "CU= =vU}@ w |Dr} RC}tm wO u}= Q}}eD uwJ &OQ=Ov |UQQ@ OQwt |=yQo =Q}t Q}=U =@ xU}=kt QO |O=yvW}B

"CU= 0 04 R= QDtm hrDNt |=ysQH C@Uv <=R= x@

|OOa G}=Dv "62 |xR=U l} 'hrDNt |=yxR=U QO |O=yvW}B |tQH Qo =Q}t |}=Q=m |UQQ@ |=Q@Q@ xwqa "Ov=xDiQo Q=Qk xar=]t OQwt xk@] 5 |WQ@ u=tDN=U l} w |O=R; xHQOR}v =vU}@ w |Dr} R |O=yvW}B |=yQo =Q}t OQmrta '|O=yvW}B |tQH Qo =Q}t uO}HvU

"Ov=xOW |UQQ@

|O=R; xHQO wO |xv=t=U "1"6'|Owt QF-wt sQH [24]"OyO|t u=Wv =Q |O=R; xHQO wO |xv=t=U C=YNWt '6 pmW

43

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0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

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1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 0 21 16 1 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 11 0 31 16 1 15 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 15 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 0 51 15 1 14 1 14 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 1 10 1 10 1 10 0 61 14 1 14 1 13 1 12 1 12 1 11 1 11 1 10 1 10 1 10 1 10 1 09 1 09 1 09 1 09 0 71 14 1 13 1 13 1 13 1 13 1 12 1 11 1 11 1 10 1 10 1 09 1 09 1 08 1 07 1 07 0 81 11 1 11 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 06 1 06 1 05 1 04 1 03 1 02 0 91 08 1 08 1 08 1 07 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 03 1 03 1 02 1 02 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 02 1 02 1 02 1 11 06 1 06 1 05 1 04 1 03 1 02 1 01 1 00 1 00 0 99 0 98 0 98 0 98 0 99 0 99 1 21 04 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 01 1 00 0 99 0 98 0 98 0 97 1 31 05 1 04 1 03 1 02 1 02 1 01 1 00 1 00 1 00 0 99 0 99 0 98 0 98 0 98 0 97 1 41 04 1 04 1 03 1 03 1 03 1 03 1 02 1 01 1 00 1 00 0 99 0 98 0 98 0 97 1 59 1 51 03 1 03 1 03 1 02 1 02 1 02 1 01 1 00 1 00 0 99 0 99 0 98 0 98 0 98 1 52 1 61 04 1 04 1 03 1 03 1 03 1 02 1 02 1 01 1 00 1 00 0 99 0 99 0 98 1 82 1 80 1 71 04 1 04 1 04 1 03 1 02 1 01 1 01 1 01 1 00 1 00 0 99 0 99 0 98 1 75 1 74 1 81 05 1 05 1 04 1 03 1 02 1 01 1 01 1 01 1 00 1 00 0 99 0 99 2 07 2 03 2 00 1 91 04 1 04 1 03 1 02 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 1 97 1 95 2 01 05 1 05 1 04 1 03 1 03 2 93 2 91 2 90 2 90 2 90 2 40 2 35 2 30 2 24 2 20 2 12 67 2 68 2 69 1 03 1 02 1 02 1 02 1 01 1 01 1 00 1 00 0 99 2 22 2 18 2 16 2 23 38 3 37 3 36 3 34 3 33 3 31 3 30 3 30 3 29 3 28 2 55 2 54 2 52 2 44 2 40 2 33 26 3 25 3 25 3 25 3 25 3 24 3 23 3 21 3 20 3 19 3 18 2 82 2 46 2 41 2 38 2 43 22 3 22 3 22 3 22 3 22 3 22 3 22 3 22 3 22 3 22 2 76 2 77 2 76 2 67 2 61 2 5

Q}O=kt u}= =@ Q@=Q@ ?}DQD x@ QwmPt |xv=t=U pw= Owt |}=Q}t C@Uv w '|a}@] Ot=U@%OvDUy

m1 = 2 062 kg!1 = 11 02 rad

sec�1 = 0 061 |x]@=Q QO xm |@=DW =@ u}tR l}vwtQ=y CmQL CLD |O=R; xHQO wO |xv=t=U?=DW |xvt=O '|]N p}rLD QO xmv}= p}rO x@ "OQ}o|t Q=Qk 'CU= xOW xO=O u=Wvu}= 'OwW|t ?Q[ u; |}=Hx@=H pm QO \ki w OQ=Ov xR=U Q=DiQ wv QO |Q}F-=D u}tR "|O=R; xHQO wO |xR=U "6 pmW

44

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0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 0 21 16 1 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 0 31 15 1 15 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 15 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 0 51 15 1 14 1 14 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 10 1 10 1 10 1 10 0 61 14 1 14 1 13 1 12 1 12 1 11 1 11 1 10 1 10 1 10 1 10 1 09 1 09 1 09 1 09 0 71 14 1 13 1 13 1 13 1 12 1 12 1 11 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 07 0 81 11 1 11 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 07 1 06 1 05 1 04 1 03 1 03 0 91 08 1 08 1 08 1 07 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 03 1 03 1 02 1 02 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 02 1 02 1 02 1 02 1 11 06 1 06 1 05 1 04 1 03 1 02 1 01 1 00 1 00 0 99 0 99 0 99 0 99 0 99 0 99 1 21 04 1 04 1 03 1 03 1 03 1 03 1 02 1 02 1 01 1 01 1 00 0 99 0 98 0 98 0 97 1 31 05 1 04 1 03 1 03 1 02 1 01 1 00 1 00 1 00 0 99 0 99 0 99 0 98 0 98 0 97 1 41 04 1 04 1 03 1 03 1 03 1 03 1 02 1 01 1 00 1 00 0 99 0 99 0 98 0 97 0 97 1 51 04 1 03 1 03 1 03 1 02 1 02 1 01 1 00 1 00 1 00 0 99 0 99 0 98 0 98 0 97 1 61 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 00 1 00 0 99 0 99 0 98 0 98 1 80 1 71 04 1 04 1 04 1 03 1 03 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 0 98 1 73 1 81 05 1 05 1 04 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 2 04 2 01 1 91 04 1 04 1 03 1 03 1 02 1 02 1 02 1 01 1 01 1 00 0 99 0 99 0 98 0 98 1 95 2 01 05 1 05 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 2 34 2 30 2 26 2 22 2 11 05 1 04 1 03 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 2 17 2 16 2 21 05 1 05 1 04 1 04 1 03 1 03 1 02 1 01 1 01 1 00 1 00 2 55 2 52 2 47 2 42 2 31 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 2 43 2 39 2 37 2 43 24 3 24 3 24 3 24 3 24 3 24 3 24 3 24 3 24 3 23 2 76 2 77 2 76 2 69 2 62 2 5

Qo =Q}t w '=vU}@ '|Dr} R |tQH |=yQo =Q}t '40 w '31 '29 |=yx]@=Q x@ xHwD =@u}= ?}DQDx@ 'Ov=xOW |L=Q] QwmPt |xv=t=U pw= Owt pQDvm |=Q@ xm |O=yvW}B

%CW=O Ovy=wN =Q |DNU ?}=Q[kdZ = 7 31 N=mkdB = 7 1 N=mkdp = 8 58 N=m

CUOx@ 41 |x]@=Q R= k C}tm '=vU}@ w |Dr} R |=yQo =Q}t |DNU |x@U=Lt |=Q@%CU= xOt;

k = !21m1 (41)

w |Dr} R |=yQo =Q}t |=Q@ =Q |}=Q}t ?} Q[ u=wD|t 32 w 30 |=yx]@=Q R= 'u}vJty

|=yCr=L QO |tQH Qo =Q}t |}=Q=m |UQQ@ |=Q@ "CU= xOW ZQi OL=w Q@=Q@ C}tm"CiQo Q_v QO = 12 rad

sec u=R}t x@ =Q u}tR CmQL Ot=U@ u=wD|t 'O}OWD l}ORvu; swO |O=R; xHQO x@ w s}_vD xR=U u}= pw= Owt pQDvm |=Q@hrDNt|tQH |=yQo =Q}tC@Uv x@ xHwD =@ "OW=@ � = 0 03 xm CU= xOW ZQi u}vJty "OvwW|t pYDtCUOx@ md = �m1 = 0 062 kg u=R}t x@ Qo =Q}t sQH 'xOWxDiQo Q_v QO sQHQwmPt |xR=U pw= Owt |a}@] Ot=U@ x@ u}tR CmQL Ot=U@ C@Uv "CU= xOt;w f = 1 1 |=Q@ '9 pwOH R= xO=iDU= =@ "Ow@ Oy=wNf =

!1 ' 1 1 pmW x@CQwYx@ |O=yvW}B |tQH Qo =Q}t Ot=U@ x@ u}tR CmQL Ot=U@ C@Uv '� = 0 03Q_vOQwt Qo =Q}t |DNU u=wD|t fdp 'uOw@swrat =@ "OwW|t u}}aD fdp = 1 02

%OQw; CUOx@ 40 |x]@=Q R= =Q

kdp = 2

f 2dp

md (40)

45

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0 15 0 14 0 13 0 12 0 11 0 10 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 �

f

1 15 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 0 11 16 1 15 1 14 1 14 1 13 1 13 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 11 0 21 16 1 15 1 14 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 0 31 15 1 15 1 14 1 13 1 13 1 13 1 12 1 12 1 12 1 12 1 12 1 12 1 11 1 11 1 11 0 41 15 1 15 1 14 1 13 1 13 1 12 1 12 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 11 0 51 15 1 14 1 14 1 13 1 12 1 12 1 11 1 11 1 11 1 11 1 11 1 10 1 10 1 10 1 10 0 61 15 1 14 1 13 1 12 1 12 1 11 1 11 1 10 1 10 1 10 1 10 1 09 1 09 1 09 1 09 0 71 14 1 13 1 13 1 12 1 12 1 12 1 11 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 07 0 81 11 1 11 1 10 1 10 1 09 1 09 1 08 1 08 1 07 1 07 1 06 1 05 1 04 1 04 1 03 0 91 08 1 08 1 08 1 08 1 07 1 07 1 06 1 06 1 05 1 05 1 04 1 04 1 03 1 03 1 02 1 01 05 1 04 1 03 1 03 1 03 1 03 1 03 1 03 1 02 1 02 1 02 1 02 1 02 1 02 1 02 1 11 06 1 06 1 05 1 04 1 03 1 02 1 01 1 00 1 00 1 00 0 99 0 99 0 99 0 99 1 00 1 21 04 1 04 1 04 1 03 1 03 1 03 1 02 1 02 1 01 1 01 1 00 0 99 0 99 0 98 0 98 1 31 05 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 0 98 0 98 1 41 04 1 04 1 04 1 03 1 03 1 03 1 02 1 01 1 01 1 00 0 99 0 99 0 98 0 98 0 97 1 51 04 1 03 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 0 98 0 97 1 61 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 00 1 00 0 99 0 99 0 98 0 98 0 97 1 71 04 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 00 1 00 0 99 0 99 0 98 0 98 1 72 1 81 05 1 05 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 2 02 1 91 04 1 04 1 03 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 0 98 1 94 2 01 05 1 04 1 04 1 04 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 2 31 2 27 2 23 2 11 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 0 99 2 15 2 15 2 21 05 1 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 00 1 00 0 99 2 52 2 48 2 43 2 31 05 1 04 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 01 1 00 1 00 0 99 2 38 2 36 2 41 05 1 05 1 04 1 04 1 03 1 03 1 02 1 02 1 01 1 01 2 76 2 77 2 76 2 71 2 64 2 5

"|O=R; xHQO wO |xv=t=U pw= |O=R; xHQO |}=Hx@=H Q=Owtv "7 pmW

�5 Q@=Q@ swO w pw= |=yOwt |}=Q}t C@Uv '|r}=Q |}=Q}t T} QD=t p}mWD |=Q@CQwYx@ |Ot=U@ =@ u}tR l}vwtQ=y CmQL CLD R}v xR=U u}= "Ov=xOW ZQiQo =Q}t sQH ?}DQDu}O@ &OW=@ � = 0 1 xm OwW|t ZQi "CU= = 23 rad

sec

"md = �m1 = 0 1 kg %O};|t CUOx@|xk@] x@ 'Ov=xOW |L=Q] xR=U u}= pw= Owt pQDvm |=Q@ xmhrDNt |tQH |=yQo =Q}t

%OQw; CUOx@ =vU}@cdZ = 0 117 N:sec=mcdB = 0 227 N:sec=m

8w7|=ypmWQOu}tR x@C@Uv xR=Uu}= swO wpw=|O=R;|=yxHQO|}=Hx@=HQ=Owtv=@ |tQH Qo =Q}t 3 Qy 'OvyO|t u=Wv 8 w 7 |=ypmW xmu=vJ "Ov=xOW sUQ"OvwW|t u; MU=B Ow@y@ ?@U 'O}OWD Cr=L R= |O=R; xHQO wO |xv=t=U uOQmGQ=N|}=Hx@=H QO |QD?U=vt Q}F-=D Q[=L Q=DWwv QO |O=yvW}B |tQH Qo =Q}t 'u}= OwHw =@V}@ ?}DQDx@ =Q u; jr]tQOk u}ov=}t w xv}W}@ |=yu=mtQ}}eD w OQ=O QwmPt |xR=U|xv}W}@ |}=Hx@=H R}v =vU}@ w |Dr} R |=yQo =Q}t "OyO|t Vy=m �50 w �40 R=u}ov=}t w �31 w �36 OwOL?}DQD x@ =Q xOWQmP |xv=t=UhrDNt |O=R; |=yxHQO

"OvyO|t Vy=m �25 w �31 =Q =yv; |}=Hx@=H jr]tQOk

xk@] 5 |WQ@ u=tDN=U "2"6Owt |=y|oS} w [24]"CU= xOW xO=O u=Wv |WQ@ |xk@] 5 u=tDN=U '9 pmW QO

"!1 = 58=4 radsec w m1 = 1 kg %OvDUy CQwY u}O@ QwmPt |xR=U pw=

46

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"xk@] 5 u=tDN=U pw= |xk@] |}=Hx@=H Q=Owtv "10 pmW

"xk@] 5 u=tDN=U swO |xk@] |}=Hx@=H Q=Owtv "11 pmW

"xk@] 5 u=tDN=U swU |xk@] |}=Hx@=H Q=Owtv "12 pmW

"xk@] 5 u=tDN=U sQ=yJ |xk@] |}=Hx@=H Q=Owtv "13 pmW

"|O=R; xHQO wO |xv=t=U swO |O=R; xHQO |}=Hx@=H Q=Owtv "8 pmW

"xk@]5 |WQ@ u=tDN=U "9 pmW

u}= pw= Owt |a}@] Ot=U@ x@ u}tR CmQL Ot=U@ C@Uv "OvwW|t pYDt u; sHvBw f = 0 8 |=Q@ '8 pwOH R= xO=iDU= =@ "CU= f =

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%OvwW|t x@U=Lt CQwY u}O@ Q[=L VywSB |O=yvW}B w '=vU}@kdZ = 310=1 N=mkdB = 281=9 N=mkdp = 41=4 N=m%Ow@ Oy=wN pmW u}= x@ =vU}@ w |Dr} R |=yQo =Q}t |=Q@ |}=Q}t ?}=Q[ 'u}vJtycdZ = 1 8 N:sec=mcdB = 3 2 N:sec=mu}tR x@ C@Uv =Q u=tDN=U u}= hrDNt C=k@] |}=Hx@=H 14 =D 10 |=ypmWOQmrta =vU}@ w |Dr} R |=yQo =Q}t 'OwW|t xOy=Wt xm xvwou=ty "OvyO|t u=WvQO |@U=vt Q}F-=D =yQo =Q}t Q}=U '|O=yvW}B |tQH Qo =Q}t RH x@ "OvQ=O |v=Um} ,=@} QkD

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"OwW|tuOw@|OOa x@ u=wD|t Qo}O |=yVwQ =@ xU}=kt QO |O=yvW}B VwQ |=y|DU=m R=CUOx@ |=Q@ xm |Qw] x@ &OR=U|t Q=wWO =Q QwmPt VwQ R= xO=iDU= xm 'OQm xQ=W= u;C@Uv w u; |}=Q}t C@Uv 'xR=U Ot=U@ C@Uv x@ xHwD =@ O}=@ xv}y@ |DNU uOQw;Qo =Q}t ?U=vt OQmrta 'u}= OwHw =@ "Ci=} Q_vOQwt pwOH R= =Q xv}y@ Q=Okt |tQHu=Q@H |OwOL =D =Q Ow@tm u}= 'Qo}O |=yQo =Q}t =@ xU}=kt QO |O=yvW}B |tQHxwqa |tQH Qo =Q}t |xv}y@ |=yQ=Okt '|O=yvW}B VwQ QO u}vJty "CU= xOQmxm OwW|t ?@U |oS} w u}= "Ov=xDU@=w sy l} QLD Ot=U@ x@ xR=U C=YNWt Q@\@=wQ R= |[a@ xm |r=L QO "OwW OwOLt |}xS} w Ot=U@ x@ \ki u; R= xO=iDU=u=wD|t w OvQ=O |oDU@ xR=U C=YNWt x@ \ki u=QoWywSB Qo}O \UwD xOWx�=Q=

"OQ@ Q=mx@ |irDNt |=yl} QLD |=Q@ =Q =yu;

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|Q}oxH}Dv "7xDN=OQB xR=U |}=Hx@=H QO =QPo MU=B Vkv x@ QDtm u}W}B |=yVywSB QO xm =Hv; R=|tQH Qo =Q}t |xv}y@ |DNU u}}aD |=Q@ |Q=my=Q Q[=L VywSB QO 'CU= xOW'Q=mu}= |=Q@ "CU= xOW x�=Q= =Q}t |xR=U |=QPo w Q=O}=B |=yMU=B uDiQoQ_vQO =@|}=Hx@=H |xvt=O x@ xR=U|m}t=v}O|}=Hx@=HC@Uv jr]tQOk u}ov=}t |R=Uxv}tmxOW ?=NDv= |L=Q] Q=}at u=wvax@ XNWt |v=tR |xR=@ l} QO u; |m}D=DU=

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