chapter5laplacetransforms(存儲版)
【正文】 se Laplace Transforms Consider the problem of finding , where P(s) and Q(s) are polynomials Having no mon factor and Q(s) has higher degree than P(s). ))s(Q )s(P(163。 1 ? )t(g)]s(G[163。0 39。39。39。s ????????? ??? ???????? 0 39。 e161e)1(Q)1(P ?? ???For (s1)2+4 ? )5s)(1s(s3)5s)(1s](2)1s[(]2)1s[(s3)s(H2222??????????i8383)i24)(i22( )i21(3)i21(H ?????? ??? 83r ??? 83i ???f(t) has a form te)]t2s in (83)t2c os (83[21 ??)]t2s i n ()t2[ c o s (e16 3e16 1e81))5s)(1s)(5s2s( s3(163。163。2 sRbYysYaysyYs ??????)(),( rRyY ??163。163。 .....)([ f ( t ) ] 32200 ????? ???????? ? ????? f d tef d tef d tedttfe stststst)()()2()3( tftftftf ?????? ???163。[cos(wt)] 22 wss??. Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Laplace Transform Chapter 5 Laplace Transforms The Laplace transform of f(t) = sin2t ttf 2sin)( ? 則 ttttf 2s inc o ss in2)(39。39。(y) – s + 2 163。[f (n)(t)] = sn 163。 ?? 39。[eatcos(wt)] 22 w)as(as????Rule 2: Let a be a positive constant. Let f(t) be given, with f(t) = 0 if t 0. Define g(t) by g(t) = f(ta), then 163。1[F(s)] Chapter 5 Laplace Transforms . Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Laplace Transform t1f(t) = 163。(coswt)+ i163。[f(t)] }wss)]was i n (w)wac o s (s[wse{limdt)wtc o s (elimdt)wtc o s (e2222saaa0sta0st??????????????? ???If s 0 )s(Fwss22 ???163。[f(t)] )s(Fdt)t(felimdt)t(fe a0sta0st ??? ?? ???? ?163。[f(t)] )]sa1(ses1[limt d telimt d te2sa2aa0sta0st ????? ??????? ? ??If s 0 )s(Fs12 ??163。[f(t)+g(t)] = 163。[f(t)] Whenever both sides exist 3. 163。[f(t)]}2 ? ?? ? ? ? ??? ?? ? ??0 0)yx(s0sy0sx d x d ye4d x d yee4 2222Let x = r cosθ , y = r sin θ sdrre)2(4dr dre4 0sr02/0sr 22 ???? ??? ?? ? ? ?? ?163。kseeeeksatfksasskaask????? ????? 1][1)]([ )(??? ??????? e ls eatatfatkk 0)(lim)( 0?163。 = 163。(y’’) 4163。(y) – s + 2 4 163。39。 163。))(e1()e1()e1)(e1(122s/s/22s/s/????????????????????ss. Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung Laplace Transform Rule 6: s1]f(z)d z[ t0 ??163。 )c o s1(1s i n1])(1[20221 tdsst??????? ???? ??. Hu, Assistant Professor, Department of Applied Physics, National University of Kaohsiung 解初值微分方程式問題 Chapter 5 Laplace Transforms a, b 為常數(shù) , r(t)為輸入 (驅(qū)動力 ), y(t)為輸出 (系統(tǒng)的響應(yīng) ) 139。2 sRyyasYbass ??????)()()()]0()0()[()( )()( )]0()0()[( 39。1Heaviside’s formulas Case 1 : If Q(s) contains an unrepe
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