◄
\ <o Oc_ t · 2 oz.3
. as Long os fC+) ,sr'l'i- t-aSt-ef" trian on. cx.poreot-,o \, ~OY eocn
~C-t-), +nc-re ,c;, lOp\oc.e do("("\a.,0 C.u('\ i q.ue)
Lii -tOY'" stob,L,h/
• \ f- ""e. COt\ find FCs) 1 \Ne can f ·, nd -f (-t-)
f(t-) ~ F(s)
. t;;o Y"OVV, +o SO\"Ve ODE) ju<;; b u~e \.Qplace t,on'5f-o,rn
i-ob\e
· laplQce t,of')s~o\'"'rn•s a.. L\NEhR o~era-ro,
➔ S\.J~rpcx;,-ao0 : -,
:t:._ [.fl+-)-+gC.t)j: 1._[f(+)j + l_[gc+) j
So :
i:-cs) -t 6(s")r / fC+)+g(+)
fl ' ) ( I ( ( I l ( ) c ( l t ;rd·,~ary d,'fferen:hat equa_-hon
· rcgo,d,n9 -t-,me dif-re_r-ent-iahon.. £> ~ int-egro.t·,on :
-, a.c;;surn-e !iri.t-iol . Cond!t-1·0f"'2_ \g (D ( some-t:::·, <ne~J
~ not-e-tnqt- rne fullow\-n<:3 exornp,es c:t-:GUm-e ,n.,t10\ cond - is (J)
ex.: Y '' C-r} + 5 y'( t) -+ ~y ( t) :. 1 ~ -Lap\ace- -t,onst-arm
s, Y (s) + 6 5 Y _C 5) -t G, Y (S) -: - ' ~ fi
1. • . _ . , ,: r • f
1• 1'SO\ a \-e Y C. S)
Yes,=
,
1 .2
S~ + ':>S "'" (q s
• -
-i:::ranstoY-mo.t1on s
-:-hen. u5e ,rnpro_per +ract-ions £{f ''+J = ~,'"2-~(<2.) --sf(o) - f' ( o '
Y[s) =- A e + ...£_ er {f, r t ) s ·= c;; i:-(s) - H o) - · ,,
- ; - - +- '5+2. s+3
t{f(t-).) :: Fce:,1
A(t;;t-2.)Cs-1-3) -t B(s)(1>+3) +- c (<;;)(srt-2) ~
A (es;~r5S-t~) +- 8( S~"-=3s')· f- C (. 5'2-+ 2 SJ
~ -there i-o ~ ~s , =v--'s~' *errn ·
Ir'\ 1
:. A+B-1-- C =D; ,5A+3B -r2C -:o / <oA:: I f-)('n ~ t_
'So A -= 1/(g j e, :. - 'I 2. j C -: '1 ~ ~ I
s
p ~ baclL in--to or19·,n.a,'-- YCe1 ..,...,, ~,~, c e .
o+-
~ --1-
s-o ·
'l<o -'h ~
Ye~):: -;- + ~-+ s""3 ~ -, nverse
J, LoplQC.e rna+lob command +o\"' fQfTIQ t..,.
!I'-( 1) + -Y2ce· 2 '') ~ \Ci3t) j
b =[.,J ~
\ <o Oc_ t · 2 oz.3
. as Long os fC+) ,sr'l'i- t-aSt-ef" trian on. cx.poreot-,o \, ~OY eocn
~C-t-), +nc-re ,c;, lOp\oc.e do("("\a.,0 C.u('\ i q.ue)
Lii -tOY'" stob,L,h/
• \ f- ""e. COt\ find FCs) 1 \Ne can f ·, nd -f (-t-)
f(t-) ~ F(s)
. t;;o Y"OVV, +o SO\"Ve ODE) ju<;; b u~e \.Qplace t,on'5f-o,rn
i-ob\e
· laplQce t,of')s~o\'"'rn•s a.. L\NEhR o~era-ro,
➔ S\.J~rpcx;,-ao0 : -,
:t:._ [.fl+-)-+gC.t)j: 1._[f(+)j + l_[gc+) j
So :
i:-cs) -t 6(s")r / fC+)+g(+)
fl ' ) ( I ( ( I l ( ) c ( l t ;rd·,~ary d,'fferen:hat equa_-hon
· rcgo,d,n9 -t-,me dif-re_r-ent-iahon.. £> ~ int-egro.t·,on :
-, a.c;;surn-e !iri.t-iol . Cond!t-1·0f"'2_ \g (D ( some-t:::·, <ne~J
~ not-e-tnqt- rne fullow\-n<:3 exornp,es c:t-:GUm-e ,n.,t10\ cond - is (J)
ex.: Y '' C-r} + 5 y'( t) -+ ~y ( t) :. 1 ~ -Lap\ace- -t,onst-arm
s, Y (s) + 6 5 Y _C 5) -t G, Y (S) -: - ' ~ fi
1. • . _ . , ,: r • f
1• 1'SO\ a \-e Y C. S)
Yes,=
,
1 .2
S~ + ':>S "'" (q s
• -
-i:::ranstoY-mo.t1on s
-:-hen. u5e ,rnpro_per +ract-ions £{f ''+J = ~,'"2-~(<2.) --sf(o) - f' ( o '
Y[s) =- A e + ...£_ er {f, r t ) s ·= c;; i:-(s) - H o) - · ,,
- ; - - +- '5+2. s+3
t{f(t-).) :: Fce:,1
A(t;;t-2.)Cs-1-3) -t B(s)(1>+3) +- c (<;;)(srt-2) ~
A (es;~r5S-t~) +- 8( S~"-=3s')· f- C (. 5'2-+ 2 SJ
~ -there i-o ~ ~s , =v--'s~' *errn ·
Ir'\ 1
:. A+B-1-- C =D; ,5A+3B -r2C -:o / <oA:: I f-)('n ~ t_
'So A -= 1/(g j e, :. - 'I 2. j C -: '1 ~ ~ I
s
p ~ baclL in--to or19·,n.a,'-- YCe1 ..,...,, ~,~, c e .
o+-
~ --1-
s-o ·
'l<o -'h ~
Ye~):: -;- + ~-+ s""3 ~ -, nverse
J, LoplQC.e rna+lob command +o\"' fQfTIQ t..,.
!I'-( 1) + -Y2ce· 2 '') ~ \Ci3t) j
b =[.,J ~
