APPENDIX 1: Useful Laplace Transform Pairs (For Test and Exam) Time domain functions f(t), t20 8(t) (unit impulse) Lapla
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- Appendix 1 Useful Laplace Transform Pairs For Test And Exam Time Domain Functions F T T20 8 T Unit Impulse Lapla 1 (148.74 KiB) Viewed 47 times
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APPENDIX 1: Useful Laplace Transform Pairs (For Test and Exam) Time domain functions f(t), t20 8(t) (unit impulse) Laplace Transforms F(s) 1 1 1 2 1 (unit step) S 3 t(unit ramp) S2 1 4 -at e Sta 5 -at te 1 (s + a)? 6 sin ot s² +0² 2 S 7 COS ot s² +0² 0 8 e af sin ot -at 9 -at e COS Ot (s+a)? +02 (s+a) (s+a)? +02 1 S(TS + 1) 10 / 1-eth + 11 Kf(t) KF(s) 12 f(t) +ft-f(t) F,(s)+F,(s) - F (S) 13 e as F(s) 14 sF(s)-f(0) 15 f(t-a) df(t) dt d'f(t) dt? dºf(t) dt [f(t)dt s?F(s) - sf(0)-df(0) 16 dt sºF(s) - s f(0)-5- df(0) d'f(0) dt dt? F(s) 17 S
APPENDIX 1: Useful Laplace Transform Pairs (For Test and Exam) Time domain functions f(t), t20 8(t) (unit impulse) Laplace Transforms F(s) 1 1 1 2 1 (unit step) S 3 t(unit ramp) S2 1 4 -at e Sta 5 -at te 1 (s + a)? 6 sin ot s² +0² 2 S 7 COS ot s² +0² 0 8 e af sin ot -at 9 -at e COS Ot (s+a)? +02 (s+a) (s+a)? +02 1 S(TS + 1) 10 / 1-eth + 11 Kf(t) KF(s) 12 f(t) +ft-f(t) F,(s)+F,(s) - F (S) 13 e as F(s) 14 sF(s)-f(0) 15 f(t-a) df(t) dt d'f(t) dt? dºf(t) dt [f(t)dt s?F(s) - sf(0)-df(0) 16 dt sºF(s) - s f(0)-5- df(0) d'f(0) dt dt? F(s) 17 S
Question 4 Using partial fraction expansion, find the time function f(t) corresponding to each of the following functions F(s): 4(s+5)(s+7) 21s+5) (a) (b) s(s+3)(8+6) (5+1) (c) S +2 s? +2s +4 (d) 10 s?(1+0.55) S (e) (f) S+1 s(s? + 2s +3) s2 +48 +20