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LAPLACE TABLES - 342 Laplace Transform and Inverse Laplace...

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Unformatted text preview: 342 Laplace Transform and Inverse Laplace Transform App. F TABLE F.1 ___—.___.______—___,____—_______ T(s) T(t) 3 i n==1,2,3, .5‘ (sway _ 01-1)! 1 ' sin at 7 52 + a: cos at 8 I . e‘” sin at (s - Hz + 02 a _—__—____._._____—_—__.________________ s — b 9 ._____— bl (S _ b)‘ + a: 2 cos at WWW 1 sinh a: 10 52 — a2 a s ll 52 _ £22 cosh a: b, . 12 l e smh at (S - b)2 - a2 a s - b 13 —— '5‘ (S _ 17)“ _ a2 e cosh at W I ebr _,,, em 14 -— ae b (s—a)(s-b) ‘1 b—a WM 5 be“ — as" 15 ~——— ¢ 19 H..— (5*a)(s—b) a b-a HArw FM LGIQ Licmfié 1' Gig/(":93 TABLE F 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 App. F Laplace Transform and Inverse Laplace Transform TABLE F.1 (cont) W TU) TO) M sin at - a: cos at 2:13 Za sin at + a: cos a! 2n 1 cos at — Eat sin at I COS at a! cosh a: —- sinh :2: 2a} r sinh at Za sinh at + at cosh at 2a 1 cosh at + 5 at sinh at I cosh at (3 - 0111) sin a! — 3 at cos at 811’ rsin at — ml cos a: 8a3 (1+ a1r2)si.n a: — at cos at St:3 3: sin at + at2 cos at 80 (3 - (11,2) sinh a: + 5 a! cosh at 8a App. F 344 Laplace Transform and Inverse Laplace Transform TABLE F21 (cant) TU) ____________________F_____.__.__———-——————-——-—— (3 + (22:1) sinh a: — 3 atcoshat TS) at: cosh at ~ I sinh at 8a3 at cosh at + (02:1 — 1) sinh at 3: sinh at + £111 cosh at (3 + all!) sinh at + Sat cosh at Via: V32: earn — COS + e-3ar/2} {V3 sin {COS (2“ + 22“” cos a2 We: Via: a (ll/2 + VESin War ---§(sinh at - sin a!) (cosh at -- cos at) 2 (sinh a: — sin at) 5(cosh a: — cos at) TABLE 1 46 47 4s 49 50 51 52 53 54 55 56 57 58 59 60 App. F Laplace Transform and Inverse Laplace Transform TABLE F.1 (cont) W T8) TO) M e-b: _ e a! 2(b—a)'\/1?§ W eerE x/E emerfva V3 6‘” {J5 — befi' erfc(b Vb} 10(0‘) 10(9‘) a”!,,(ar) Jo(a V r (I + 215)) J.J(a\/r2 -— b3) r> b 0 r < b (JAG!) (.52 + “2):” a M .._...:.‘__ (52 + a2)3,’2 ___'______‘________________.__._.____—.__—u_—.—-————--——— ”0(111') 52 (52 + a2)3f2 1 r1102!) (5 2 __ a 1)3,"2 a M John) - aIJ 1(az) S (52 _ a2)3,n'2 W fiduf} 346 Laplace Transform and Inverse Lapiace Transform App. F TABLE F.1 (cant) M 11(3) T (r) 61 W Ida!) + Gilda!) MW e" ’ cos at 62 -—J _2_‘/— V3 Vm Mm 63 2:1“. sin 2%? s“ v; W {fa}: I m": 54 s~+1 n > —1 (E) Lax/E) W 65 e-aV: 6—8/4: W Van W 66 mar—“G a (“1M 2V1rt3 M l r“ 63"” I 67 s erf(a/2W) W 840% - 63 s crfc(a/2‘\/§) ———————__._._.___._.______________________ 69 (av; ebw‘m erfc(b\/E + i) VE(\/} + b) 2% W + — _ -u! 70 ln(s a) Lbf—L s + b t W 1n“: + a)/a] 71 u:— Ez' (at) W ( + In .9 72 — 1—74 Int 7 = .5772156 . . . M m —2\/¢': 73 e crfc(Va/s) ‘ V3 V17! M 74 9‘11““: crfc(s/2a) .216—312 I TAI 75 76 77 78 79 80 81 82 App. F Laplace Transform and Inverse Laplace Transform TABLE F.1 (Conn, 76 78 79 80 82 -83 84 86 87 89 7(5‘) 8’2““: erfc(.r/2a) s e‘" erchas W 9-0.: sinh sx s sinh sa sinh sx s cosh sa cosh 5x 3 sinh as cosh 3x .5- cosh .ra sinh .rx :1 sinh 3a sinh sx _ :2 cosh .sa cosh sx :2 sinh sa cosh .rx :2 cosh 5a cosh-:1 .93 cosh sa sinh xv; cosh av; 31:) erf(ar) 1 Vr'r(t+aJ 1 r+a 6(1) = delta function 6(1 — a) x 2 " HI." . mrx mrr 2( )sm-e-cos— a 11,.-. n a a 4 .. (—1)” , (2:1— 1)?ch , (Zn—1hr: ;n~lZ-2T:T)sm—-20—sm—T I 2 w —1" mm, rm: ——+——2( )cos-m-smh— a Turn-1 n a a xr 2a m (—1)" , mrx , m7! - -—1- 1 Sin—sm— a 11' ,.-1 n a 0 8a '" (#1)" , (2n-—1)Trx (Zn-"1511'! -—--—-—— os——--—— Hm: ——c 11'2 "-1 (2n — ljl 5m 26 2a :3 "" ——+—-—2 cosfl(1*cosfl) 20 172 .-. n2 a a 8a .. (-1)” (2n — 1)-rrx _ (2n — Um t+ “2'; (2n _1)zcos 20 SID—2a 164:2 2 (—1)’I 5 (2n - Um: I 2 _ + 2_ 2 _ 2(1 x a) 7T3 "a (2n _1)3co 20 a: 2 2’ 2(w1)”ne-"2*Wz sin ? n-l (2n — l)1'rt s — i v. E r E 3' ‘7 i. ‘; 348 Laplace Transform and Inverse Laplace Transform App. F TABLE F.1 (cont) ‘ 7(5) Th) cosh x\/; 71' ' 2 2 (2n — Um: I __ __ _1 n-) 271 _ 1 —(1n~1)u2;;‘4n — sinh (IN/E a1 n2} ) ( )8 cos 2‘1 91 smth 22(—1)”‘“(1"‘”2“2”‘“2 sin (2n .. 1)arx V; cash a% a «=1 2‘3 cosh x‘\/.; 1 2 m 1”; 2 mrx 92 —— _+_2(_1)ne—n rfu cos_____ V; sinh av; a a "-1 a 93 -———-—-—-——5mh ”W: 5 + 3 2 ("1) e‘"2”2‘/“2 sin fl 3 sinh a V; a 11' n-l ’1 ‘1 94 (:05th 1 + i °° (—1)” e_[2n_”2w1n,‘a2 cos (2n — I) m s cosh (2V; 11' mu (2n — 1) 2a 95 smhx‘V—s 3+2 (”1) ("213,1“sz mrx :2 sinh av; n-J a cosh xv; 1 16a2 .. (-1)" 1 2 2 (2n — Urrx 96 __ _ 2 _ 2 +t""'_ _— -(2n—U1r rim _— szcosh (IV? 2(1 a) “n" "=10?! “" Use - cos 20 ' °° -A§1/02J A 97 100$ W) l _ 2 E e n( ”XI/fl} SJQGG VG) 11¢] )tn-hb‘n) where A1, A2, . . . are the positive roots (£100) = 0 Max Vi) 1 °° e“:22'/"2J0{A,,x/a) 98 —-————- -Jc2~—c22-+r+2«:22 —— 311000 VE) 4i ) .21 A3J1(A..) where A1, A2, . . . are the positive roots of Jo(/\) = 0 R E F E R E N C ES 1. C. R. WYLIE and L. C. BARREI‘ Advanced Engineering Mathematics, McGraw—Hill, NY, 1982. 2. M. D. GREENBERG, Foundations of Applied Mathematics, Prentice Hall, Englewood Cliffs, NJ, 1978. 3. M. R. SPLEGEL, Laplace Transforms, Schaum's Outline Series, McGraw-Hil], NY, 1965. D. POULIKAKOS Mechanical Engineering Department University of Illinois at Chicago PRENTICE HALL, Englewood Cliffs, New Jersey 06732 ummm. a “24%.“; Lfiul‘f-«LLA—Irrm -=..-.u'.~»,._.+..4 ...
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