Question

2. Find the Laplace transform of the signal f(t) = 102–2014,(t) + 15te-20)u(t), a) with using tables and properties. b) without using tables and properties.

Answer 1

Sol -204 u(t) + f (t) = 10 e ad [st & 20t Juct L.T -at e ut) sta L. T d x (t) SX (6) dt 20t u(t). ot ] e FS) 10 -L Lo T 5t S. s+20 XS) aD d X (s) as - 20t 5t e a 15 . as S+20 5 5 d ds G 2- st20 (s+20) 55 : F (3) = 10 + (5+20) (S+200² 155+ 200 F (O) = 10(8+20) +55 (S+2002 (51 2022

fe) = - 20t 10e att ď (5t e 20t ut) at -20€ u E) (e 20t) - 20t + dt 11 at 204 -20t t (20) e -20t = 10e ut) + 5 su u(t) -20% = 10e - 20t -20t u(t) t 5.e ulta 10ot e - 20t u(t) - 204 15 e u t) - 100t -st dt e F 6): Sze - 20€ -st 8. e dt -20% -st dt - 100 10 Ste e 1 15 e -(st2oot dt & +(6+20) t at - 100 - s e 0 -(5+20) t (5+20)+7 x te at 15 e 100 0 - (s+20)

-(s+20) Now) -(s+20t ste -(stadt D e cst zoot + -(s+20) 0 2 (s+20) - (s+20)t 0 -(s+20) to -t e (s+20) S + 20 (oto) [ D (s+2017 (S+20) 100 15 - F (s) = + 6+2002 S +20 F (S) st20 رہ رک)

100 15 (8+20 s+20 15.(st 20) - 100 (s+2oj2 = 1s + 300-100 (s+20) 2 FC) 155 + 200 (s+20)'