t.-l ,\l"- r"

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2 5. Laplace-transzformrici6r6o.L-'{+4 F-} -.' {,+} ., ={,,'_r}: (-5cos2t)*(sht) =-5/'.o"Z".sh(t - s)ds : cos2t - chr.16l.L{cbt * sint} : ,C{shl* cosl}; igy a T 25.19 t6tel kdvetkezm€nye szerirrtchl * sinl: shl * cost, ha I 2 0.162.lsini. Megjegyezziik, hogy az inverz Laplace-transzforrn6lt kOzvetlerriil kiolvashat6a transzform6ttak XIL k6plet6b6l, hiszen (-rr6s,(r2e3r) . " o, = (t' _ 4* 3\ .t, * ( -f\.-ar\7 49 343/" \343i{ffi}164.+(ch2r-chr), mertpr. F(p)=@ ;@ _q: (*-fi): r"r"*1 I/ I 1-)165.C6lszeriieu T 25.30 felhaszn5" tasava. -- ..la.lik. (u"' ^,fl t \l= p-, + 1/ezert- , ( 1 ) r . ( r ) t l.-'tF-l= it.r'r-sint) igy c-'t#Tl - (j,.r',-.r,,1) .(|t.ft, - "t"tl), ami T 25.9 szerint a 43. ds 48. feladat is sht * shl kouvolfci6iravezet.166. Vegyitk 6szre, hogy a tnegadott I'(p) ktinnyen integriilhatci, r1s alkalrnazzrrk aLaplace-transzformalt integr6l6si tdtelit, T 25.25-t:rttt = tr, =, U,- A!n"\ I,, {":,}az el6zri fcladat egyik r6szercrlnrdny,irek f, lLa'zrr:ilisival.167.1 | I \' lr r \'- = lp3.(p I l)3- \prp*rfi : -r_1/\t- l r(srr, -.i,rr)IV6gezziik cl a kijelolt hatviDyozasr €s ism6rcltor (},.,}u-nctgyel tijrtan6 helyettcsit6s6t mi dcnhol../-t2 \ //r \t-'tFtpt\ =,-'l rr-oJ ,r (:-3t.6)#)168.e(p)-t szorzatk6nt d.ri,, ua. {p =ti .i*\' r-, I 9'11'),t} - f .r,r.etp) ,jr-r,'''' - [atpt'".1 Z-169. 8:slrI+:cht.lTo.Hardrozzrrk r11cg et6'szcir a-,{*;il. ,,} ,11 1 1 I p Il 1p(p+1Xp?+1) .1p 51, + 1 - ?0/ + 4 - 51,, + I25.22
I17l.,t DiIr.- l-|l(tItc'I,rlace t rarrszfr;rrrtil I :!c-tt-t/2) - fi cos2(r- ])- $.;,,:1r _ ll). f,"i, 1.. .{ T 25.21 }on\.drici6rrir(l sz.rirrr {-rlhar
Page 1 and 2: Laplace-transzformici6 (nregoldisok
Page 3 and 4: I20. sl'(3i - iJ:' (t3t-\ +."r-3!)
Page 5 and 6: 25, Lapt!" r rarqzfofu,in.i,i37, ct
Page 7 and 8: 63. A r 25.12 t6tcl szcrinr LLf') -
Page 9 and 10: A.zr eftiz6 fclad a t rn"gc,ld;is{l
Page 11 and 12: L, t'.pr :.93. Alkalmazzrrk a T 25.
Page 13 and 14: T 25.21 szerint 6s a t6bl6zat V., r
Page 15 and 16: !u,LapracP traxs7t,,r,,,;. j,lps I
Page 17 and 18: 25. Laplace-transzfornuici6L27.t |
Page 19 and 20: l,aplace-transzformAci6tt'lrit a lr
Page 21: I-Izs. r.^pr.*,t.""-i.,",a.i0!I 155

t.-l ,\l"- r"

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