jt .; u: - sogangmaths.sogang.ac.kr/jlee/syllabus/09-02/fm/fm-solution.pdf · i . :#1 . u",...

13
i . :#1 U", =- Ll · U , . 0( : o A G : -kw '\" = Jt .; u:: 2 '3.;- "f"-/s 6 A::: 'r« 5 ttL- hMe cJ tluz-f ·1. 1 U- hei'j lvr "f 'fvwer U/.U2, tor11l\hJa.. s := U t + C\t e, h Dh 2bntf-A\ -tot1\11-\..14 .) U t CC ') .1. . t =- u.\), c -t '2 QJ l; - 0( t -t -i . :=: - 5 x t -+ x 5"

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Page 1: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

i .

:#1 U", =- Ll · .().~t o( U , .

0( :

o A G I~\'· : -kw '\" = Jt .; u:: 2 '3.;- "f"-/s

6A::: 'r« 5 ttL­

~) hMe cJ tluz-f·1.1U­

Q» hei'j lvr "f ~ 'fvwer

U/.U2, ~ VO/l~ u..Q. d~~+~e tor11l\hJa.. s := U t + ,~ C\t e,

~ hDh 2bntf-A\ ~'~ce -tot1\11-\..14 .) ~ U t

CC ') .1. . (£t'~!)... z» t = - u.\), c -t '2 QJ l;

~ - U"~ 0( t -t -i ~ 't2-. t~

:=: - 2~. 5 x ~ t -+ ~ x ~. 5"

Page 2: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

.; I

:tf:.2lp,b/ M2.)

. (l CAA 6) ~M.d \ 000 k~

• '\J ~ 2..5 ~s

• )\;.. 0( =­ it. EVla-I~.e pllwer :::. ~t+ k 'N

~) ~ .e.s~st-1Jt4A u. h. tIu- ~ hl1Y\ ? l~ l1t-fu ~ '1 10.. h,~~/ ~ ro~.l ~ h6V\~~~

cu.auMIV\1 Rt.:1 ~"W\1~ flV\.'J- -tea. In:lf..A.J-. w..e~

<;o~

\().) EY\~ Po\AJ.-.lA. =- Rrrc-e. x ;4 p...e.e.J.

~4ooo - ~ x: '\J z; ~ .x.2-S

.~ 11 - .2..4-1100 _ Cf 6 0 -.! :tS'

- II :::. 1< -r fh~ ~ t>(

R ==. T\ - fV\~ ~ b(

\ ..:: Cf b0 - looo X~. 8 ». TZt­::. 260 I

Ii - R ~ F = I'ha"

460 - 2b 0 =: 100 0 0..

-.- a..;:::-­

Page 3: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

• •

.\ .

\~V=3

<;)..- TtJ<e Y'nD M.e"h lO-) /

Page 4: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

'. .

=1t4. 1/'"'(0) = \0 rF -+ 7)° ." 0 ./

It- -:::. 41 -\-3.f ito) == o , .

~) IH4) (\'j l 0 t 'l-) I SDI I}: =- 4 It + 5Jo

)0/ J; ::::. ~-t.-+ Cl ) 0° -+ l3 i:- t c:J.)Jb

/ 1..... .

• 0 0SlVlLR. rtv) ~ ([)..; C1= (2 -==0) lr:::. 4-t II -+ ~ t J 1t-(4) :::. I c ~. + 12jD --:, (c..)

Ir- -:::. @t:l-t dI) It -+ Q:-t'2.t- J2.)J S,nCQ Ir[D) -= 10 11°+ 7Jc) d == 10/ d. -=- 7

l 2

-: Ir = (2.t -:L+10) 110 -+ (~ t ~ ~ )J/' /rlf) -=. 4 2 ,0 + J ',f

111"(4)/ ~ J42"#+31"- = 52, '1. __ ([")

F"lnJ.. l"-) c....J"'rf 1YIM4. (x) 5) (~ \,J~', £e. h~B lYJj tDlrQM- A/

iM ~u;Q; brilAWl/ fWd ~ Ct~Ie.

k-~ AS .r cLow"W<1A<{ l/-"-'lh'~L ['< L-tR"R'ttlo t>f 32 4g­ f}oYV'\A..<IA

cL's f-WIIL e ~ YV\1Il AB X­ I) 4­ct'sf-C{V)U2 1YlJt1" Bc.. I c 5 I-~h n& VV1tr»1.Qvt"kJ tt-bo wt A Bj Bc..

3.1 X -+48 *5 =­ 80)( If ~ x ~ J.E;

32 f -i 4 ~ )( 6 = ~)( 5 ~"1::::- ?. 5

Page 5: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

Q€C D [V I~~ ~h ~1/ '1 -h. it.a. I'" &,.l'\.l..J. r ~t1 ~ LVe.. ~ 4{- I 2... ':1.q.R::. rh j C-lR I>( -=:. 2 j »; '3 ::: 13 ~

F /M R =- i .~ ~ ~ ~~ j

W()I-K ~e ~~ 1h\~

- FUl'"L-e )<. cL~rl-aMt: €

= F;t =. -!2:-. ~ ;t

13 .

Now/ 3tA,n~ PE =- n-'l5 h ==..2..~'X~~

::: ~~)(

IDst k t ::: 1: W\ 17:2-1-;

2.. ­=:-L rk _c. '1. = J. -2'5 =2!:>.2. 7 2

Work - E"'e~ P/\~u.,!-e./ ,'N6rk dtJ")le e;;~f ~r~~ _ 1S I l"I-P.:.t.

, ­ . lost- kt; - d~ Pf

,\ E lj X ::::,)..r l"!

..­ I) ..1 X -::: .2 5",,'22 ;<. ~ "::. I. t)D 7

:::.. t\ 5 "'V

Page 6: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

:#7 (P.51 1J1 ~ cp~

CIA) "i =:?" rlf"B =? ,

(1,) w~ to.s 1- k E -::: -h 1t\f1~ /(E:.J

~D! (n Gr,s~~ Oy fl.-r'LlAA M.oO\.AAf-uttt

mI l1t +flA2 U. 2. =- 'Mt- '\Jj +11\ 2. ''It.i .: p( V = 1'1JA -+.2/ ""E ..'- ~ -r~ ==v

V,) ~.ew~ ~h~

'\f~ 'llB-~ e= 'll~, -::: y

..', '\J": .... T"" c» VB -'VA = '­~

In ~/ ~::: j U-2e) Y

VB ==. 1 Ut e) V

1y):~J k E

=- ±/'Itl u,2- -t l M;l. tL2.2­

:::: 1: M VJ... -+ ~ .2P.\·O!L = i ~ Va,

::f-' 'Y\~ k E­-L A'-'>- 1 '2..=- 2. ~l 'V, --\- 2. M,2 1T.,J..

==- ±t\-t ~~ -t { 2." 'VB:L

-.1.. I ~V::t. I -v: - .2. m q (1-:2.e) + Yh. ~ L(f €)

1$1 tl4Au.mp+-l~/ 1~;h'A..Q icE - ~'.y,.J2 k t­

- lust- kE ::::. J. »c 1~;k.,J) kE

L.

Page 7: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

[")Ca."" ;"',,)1 ~ c::9" P:'f-" r ~ (M-ecl",;U ))

-tt=1

h~ ~ UM.f--"" cfb M4A4

n,,~..J. 2tMtu .( ~fl~~ A

M =- 2 , ~l-A 13

(~ \"" _ >-... 0tl\- _ :l ..Q..xt-~ 'A - 7 - >... L -=- 2 ·T/?,

L-x:

p

~ li) ~ =(;UM~ httLe.­

QJ) ~; orJ.- '1-1\-tv -h~e

~ 4U = 'bWW \A = lnlf-~

::::z:t;L t. L-Jt =- 1[

-- W::II l-t~1) 3 =£

l))

IT OC I3

1- =- (A~~ t) = ~ AM-(1L~)

-h." x=\2 2--~~

. '~l= 21 -_II

k~~h ( £I\.QA 91- rt> P~ -;,r ~ C

kE = ~"' 1l"~" ~ "'~W~l~'-;L") ~ ~. ~ · [~)'- ( 2'-1') " ~:

Page 8: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

tr-~ m>J.

~) G,~ tt = C-tmsfMVt/ S-l:lo) =- ?

") 0 = I 0 + tt . .:10=- 10-+ o.-t. ­)

, 1\ - i.... ~ (,A. ­~

\~~(.Q 'V = '0 +1:. S = lot + ~ ..e­

, _ S ( ~) = 400 l'V\.

,)r c< ={ (1;,:::. 7\.: ' / \' '

(jl) S (>n) = ?

o = 0<'-1- ~ ,.lO

t = ~ V=- ,0/

-===;?i ?, 0:::' 0(''''0 -t ~ ~ . :.La::" -t I 0

S=~vdt ~

S{~o) -== 4ib~ 3

Page 9: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

II d ' ~ f1-t,bl~ sk"ul& ko reAJ a. = h\. I Ll4.. DJ­q~lA..1.. r'h D~~ I I

~-r--~

""'j ,J"r s~ co '"fJ M5

rL~: (t>0Fp =? \}) OC =?

solt-d-t ~

Page 10: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

~)

'\)~~ tAl- (G~ (A)'J. - x~ )

!\J = tVVr\A X ~)( -=:. D

It '\J""'-o

s /;.Lnj

, IS (6lltlh~~) V" ,",-* -s

--.I~-~-_.:.....!....--

0-) skol-0 ~ =- i (Y) F~ '\J~ ~ t~ IT) ~ ~ db Q

1 V "' 2., 0...~) W~ ~ ~~~ v.JOCA~ ~ B t4 ~ ~ V \111\ +~ t>-t ~ ci «

)~ AI~ A) ~~ ~t :=- le:d p£

~ --= fA ClR r{ - C\. Ct:R ~ ~ 3

4- ~ - UR~ a.

o.~~

, 1\J1-= ~~(A(zf -~~ ) -CD -V:l-At IS ~ =: yY\ ' 0: ==- rn~ ~~ /

-.•

112-

= 0ct~0' - GJ

CD -t-@ ~ ~ :c:- ~ . ' . ~=- ~

MtfYeo~ ~'2..-= ~ ~~

Page 11: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

l~ kE :::: ~ fE~c / i W\ ( V~ 1J2-) =- M ~. ~ c-;

=7 V L~ ~ f!J ~ A

h ~l. ~ (~' 1-~ {)1 twva-J

LJSln, j: 'YVf-e-Y'~~ ,

Page 12: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

-----

" .

'pJ-i'o q-.wtA4 ~l[rl

W G ~ ~ uJ..f/\j tt4 i'YVW\ c ~ x

It-e.. )0'J l-t-t-x)=i ~kl~{+,,)

i-t?-- .J.. x ~ _i h'2. + . ~ hI< 12 ~

\ -.l 2. .l h 2­l-i lo, + 1 J -X -=- 2. R.. - 1'2..

~ 1 :L~ .{ ~ '. rv '- 1\.-=

,.f ~ -t 1'2- ~

l"-) <h~w ~ i c£..'-"> h'.1 -J{\IS ~~ I,tl Ut... r~sf- I~ JLc..~l \bY\ ·Ll\rvv t-\ h/)n·2~"",~.JL rl~"e w~ ~ ~ . 0 In'\ , "/

SV '-~~ lJt> fu c.yIIVlt!~r hl,.lvk l~l llvz. r/a.h€.

C;o ~ r t '2-_ \...'L. - X~ 0 _ ~o

4 h.-l2 i

\0J ~ ~t..t--\ c"r\\'\/lko L4 ih ~ ey ~I~ I

Page 13: Jt .; u: - Sogangmaths.sogang.ac.kr/jlee/Syllabus/09-02/FM/FM-solution.pdf · i . :#1 . U", =-Ll·.().~t o(U , . 0( : o A G . I~\ '·: -kw '\" = Jt .; u:: 2 '3.;-"f"-/s . 6. A:::

-----::.-[zto