I,IA?H 2S6Exarn IIIDr. lvloha.mrnad I(havaniuSHOlry YOUR IMOIdK
(Prs)
(10) 1. Find r[/(r)1, rvhere i(r) = {1,' ?:i."'{ 1t) = t U(t- -) = tn 7(t) , n; tt
Yo{+ 3t'1. f ,)" G,nrr) = (- ,), q,n Gr= f\"+t)t
(10) 2. I)etermine Llt' - fer + e4t cootl.
NAI,IE ,K!t.,nttlo * '- "ru *r *: ..
ql+\=t1(t-z) / ', G(s)= {'': (- rr J'n f a t\ [ t-,' ^-',1- r'' .r.,F)=(-') i*;t- i
.L-1)
I
sb\)
>,1
/-'IroL
s- !---[s-,,)t t I
(10) g. Detelnrine f-' I u ltr* | .=lLs'+4s+13J(StS= sL+ks+rr -) st+ks+t3: (s*.f tq
t-'f 3srs l= t^'L' L *-t*'l I o(J 3s+ 6 L-LQtr) tq(s+r)z tt:I F)t (+)StZ
I ss*-s IL (stz)"+q J--1
I2l l_. ? 2. I\s+z\ f3 \_l(si-|'*r'
\t3-t.*, {*rt} =
(ro) 4,Firrri /t'l#A]
(1u) o.[=o]
p,s'+ trA 1- rls'+ css(s'rt)
A + Bs*C Is s."t lt-'l'lA Ipl
L
C= o, 6=-*-t'E l-)4'/r - (v,). Is F;.]-,/-l*;. /;'iLg/1!r.l= _L-\, S \l:\*,rutlirrl= +.j --s1* ,t ,/\-b-- c
**, ( t'* ,l(:'+r) -(10) s '-' ['. (H)] [k,.d\ l{t +rt)i= F'i r) = -+f,"= i- "fr 'L'lt'{t+ro}]='{*.#i
-> t {f0 = *z- sss[rt) a- 'i-r's (t)
*) Zi+tt-oo5t"'! =[*\ r(")a"Js
*c,cr[A -l F(*)= *
nr;rt = tilIJ = -rfnt,7L
,\ .b1 + ,1(-, t\i
L t t-t"'-rJ
f i, -g*rd,I \o ,t^L+r \,/s- J1y= ..'+ t
4u "- L" da
1.N **=E
r\\ .
t*r,a- + t
Ot t {(r)J =i+ "[(r) = r
"url"l : ul ,;r,laL-t-l- L"J t/,V nle/\n l@-) j, U *"Jr$"bl,^\ - +t
I
S,ffi-!,n*rplfrl +r) re- ,e" [t)
{2A} 7. Solre t1' the method of Laplace T\'anslbru the iuitia} r,alue probler rr;,1" 4-Ztyt - ,ly:1y(o) : tl; y'{tl) = o.
&1r"\ -z {ris'Y(i -sylo)- v,lo) t"\ v\'- {r,)
, ,lty'j ,, /r\v] , t"\t]
^-r,L .
LtPt*a,E Dop.,inr
It* y'l = Gr)"+o)= *(civ')) = -*(,vr,l-rr,,: -Yl'l-'Yh)
e st [,) ,A W *.(-, y,(,) -y,r) - { /r,r =
(i) + yr(s) =o3t^('\ - s7v\-_a -J+c
\s
21s) =
("*) r' +c
\5
LI-t*
7z -s/ue-lL,I t -5/EI se
I
- z rlr(s) =[s"-i yn>(+ .*)Y
y(,\. uJt+- i)d' _YG) = J ,nt ?() d,
L-S stn
-))\
g s'1,se
Lt -s /,,:5eal
-s /q,l-se ds +c-;
Itn ordut (sot'ilir'og)orTe
-JZs' ,1trs\
j,/ (tZt
-5 /yoL C
&*\
\ - 5ltlSE
wlr.t f[..coru,yn I
4s- -/
zts /q
= 4 +ce-s, -F,. -s"/qs'e
Y (t) (sor",rncd ilr LNtaLft o"^*,;rr)
C v-rrsf \",
+4*! -t-t^t ont rr*ws'.
!/r1 =6 , ,.!n90r9@
zt:
J.5i
s' J z
I .7,)',lL+qe* ) +\r3 -sl Ito
ob