Use table-lookup method to find the Laplace transform F (s) of the following functions in domain:...

 

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Use table-lookup method to find the Laplace transform F (s) of the following functions in domain: (a) f(1)=(+41 +2) er (b) f(t)=6e" cos 21-e (c) f(t)=sin (5%) (5%) = [HINT: cos 21 cos 1-sin t; sin + cos = 1] (10 %) Laplace and Inverse Laplace Transforms First and second order transformation: L{f'(t)} = sF(s) f(0); L {f" (t)}= s F(s) s f(0) -f*(0) Laplace Transforms f(t) 1 t Inverse Laplace Transforms L-{F(s)} = f(t) L{f(t)}= F(s) F(s) n! sin @t cos@t 1 s-a n! (s+a)+ S +00 sin @t cos@t (s+a)+0 sta (s+a)+0 sinh t cosh cot sinh at ecoshcar fsin cor i cos cot @ (s+a)- sta (s+a)-w 2 cos (5+00) (5+00) sta -- 412 a f" (nis a positiveinteger) (n-1)! sin cot RRRR coscot sinh an cosh cor Use table-lookup method to find the Laplace transform F (s) of the following functions in domain: (a) f(1)=(+41 +2) er (b) f(t)=6e" cos 21-e (c) f(t)=sin (5%) (5%) = [HINT: cos 21 cos 1-sin t; sin + cos = 1] (10 %) Laplace and Inverse Laplace Transforms First and second order transformation: L{f'(t)} = sF(s) f(0); L {f" (t)}= s F(s) s f(0) -f*(0) Laplace Transforms f(t) 1 t Inverse Laplace Transforms L-{F(s)} = f(t) L{f(t)}= F(s) F(s) n! sin @t cos@t 1 s-a n! (s+a)+ S +00 sin @t cos@t (s+a)+0 sta (s+a)+0 sinh t cosh cot sinh at ecoshcar fsin cor i cos cot @ (s+a)- sta (s+a)-w 2 cos (5+00) (5+00) sta -- 412 a f" (nis a positiveinteger) (n-1)! sin cot RRRR coscot sinh an cosh cor