
 !"#$%&'()*+,-./01!"
#2!3&!"456782!39:;
 /<- 4 =/*-
 -/-   >/?-
@$$9&AB BCDE)B)
 -/FGHI5&AJ !3G
4 >/%GHI5&JKGLM
 =/@N%OJ$)P
 /%Q&ABR$QSATLM4A,)4A$)GH.
*LC%TL$LM&U1:!VHN45HLC/>'LC&D
!V* N45LC/0A(:!V)
 >/ 4 /*
 -/  =/7
W$9&A3B$
)(20cos)
23
sin(2 cmt
x
u
π
ππ
+=
X&$)
"Q:GHI&AB)L'&1B45:$%YD,./ZC
&$&AB)
 =/7 4 /W
 -/*  >/+
7[\GX]^,F.X\H)
)(100sin2100 Vtu
π

Ω
 -/
+LC#cG!VLMG!V& gD]^,./0"Q

LC$
)L)Qc!V "Q



NW,.)g
 =/
)(210 cm
4 /
)(35 cm
 -/
)(310 cm
 >/,.
6LC)cG!V& D]-,hi^W./f"j!3k$
 =/
2
2A
L)L

l 4 /
2
A
L)L

m
 >/

/  >/X7/
<
/
0Q-L)=&AT!M$v$!3GXK4AX4!M$)/
4Ae&/Q%-7X%=*7wLM4A45
 =/ 4 -/
 /  >/s
0&)XLCeQ3G(%UALC
 -/e 4 /$%&'x_
 =/45  >/$%&'M_
*%Vby21:T&1$$\y-]+

X
$$$%&'(QJ45I$\y/\_:21)g
 /X7
2
4 -/
2
 >/
3
  =/X7
WQ24!M$)!3AH$Q
 -/NWH 4 >/2AH
 /2AWH  =/2AH
7!"bC$]7y%LCy1QLd&%\LM
4%)/=\LCT%LC1X7X'1$A(7/)yk:1)
 -/4 /
 >/7  =/<
+z:LCy1QL!"y%b9dQ(C)
 =/NCX!3LC 4 /NNX!3LC

:_1Xe€LCL))X!"_NL}&q&A)L)_GWHNJH/0A(:
_1)
 >/ 4 /
 -/X7  =/7
FQ%u

Xu

5&A&U1L)d4A_1U$U>]7G/@N
%9u

\_145/QN:u

Xu

&K N%Ou

u

)g
 -/6 4 =/+
 /*+  >/7W
*0&1%%Vb:•B!3N%OLB%
)/0&NOQXad4ALMLB&BL)%LB&BH!3+
L)$4ALB%;
 -/?LB 4 /6LB
 >/LB  =/<LB
W&Vc$\OL))ZX]+X+7/
s*W
tX]*/

 =/` 4 -/7`  >/7`  /`
?01_)BGN)1_:IL)&Vc
 >/•%_14 -/@N2BDA&_
 /$%U„  =/)G%y_
*=QS1:U&$y]…
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,^/
+
.,./0"Q2!39
452!3HA)
 =/X+7/
s6
,. 4 >/7/
s6
,.  /X7/
s6
,.  -/X7/
s6
,.
*! LwX4\[]•X]^,†ƒ.X‡]7F|Xˆ
-
]ZXˆ
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2
ZX
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G7^/0 ;  

 >/NCX!3XMVLC
*6[\G$1N%XOA%%\NH
# \C)B)
 >/_AU2\(&vN
4 /GO\HNL)\HN
 -/0e&dNX$2
 =/GO\HUL)\HN
*<!VHq4%1[!3T5XTGND!MA/eHL)!V_
x&$\_/0A(!V!V:!V$)
 =/
1
+
n
nR
4 /
1
+
n
R
 >/
2
nR
 -/
n
R
2
*?=A:!‰4SGUL)
 /o4H:(H)%UALC
4 =/F%:(N%UALC
 -/=A(H)%UALC

Ž
*!V
Ž
‹ !‹ ‹ X!V‹ A
Ž
LV
•
Ž &A
4 >/• !V
Ž
‹ 42
Ž
*!V
Ž
‹ !‹ ‹ X
Ž
A
Ž
LV
•
Ž &A
 /• !V
Ž
‹ 42
Ž
!V
Ž
‹ !‹ ‹ X
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A

 =/!" 4 >/!"G&4
 -/FGc4  /!"{
W<\v"%%VbP

]X7†L)P

]X+†L)c•B%X)%
c/SD%':OLB%$)LB&B),A.
 /D]*,. 4 >/D],.  -/D]W,.  =/D]7,.
W?bV&c&%X%SA LM’0/a\%
QHALM] ’:b$)
 =/0 4 -/0  /0
2
 >/0
2
7\H!3L):\4)y4SD9$H‡
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,F|. 4 >/‡

 /<- 4 =/*-
 -/-   >/?-
@$$9&AB BCDE)B)
 -/FGHI5&AJ !3G
4 >/%GHI5&JKGLM
 =/@N%OJ$)P
 /%Q&ABR$QSATLM4A,)4A$)GH.
*LC%TL$LM&U1:!VHN45HLC/>'LC&D
!V* N45LC/0A(:!V)
 >/ 4 /*
 -/  =/7
W$9&A3B$
)(20cos)
23
sin(2 cmt
x
u
π
ππ
+=
X&$)
"Q:GHI&AB)L'&1B45:$%YD,./ZC
&$&AB)
 =/7 4 /W
 -/*  >/+
7[\GX]^,F.X\H)
)(100sin2100 Vtu
π
=
/

+LC#cG!VLMG!V& gD]^,./0"Q

LC$
)L)Qc!V "Q



NW,.)g
 =/
)(210 cm
4 /
)(35 cm
 -/
)(310 cm
 >/,.
6LC)cG!V& D]-,hi^W./f"j!3k$
 =/
2
2A
L)L

l 4 /
2
A
L)L

m
 >/
2
2A

<
/
0Q-L)=&AT!M$v$!3GXK4AX4!M$)/
4Ae&/Q%-7X%=*7wLM4A45
 =/ 4 -/