Find the Laplace transforms of the following L {e^((-6t) sinh(2t))/(e^(-6t) cosh(2t))}

Tahmid Knox 2020-10-27 Answered

Find the Laplace transforms of the following
L{e6tsinh(2t)e6tcosh(2t)}

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Expert Answer

grbavit
Answered 2020-10-28 Author has 109 answers
Step 1
We have to evaluate the Laplace transformation L{e6tsinh(2t)e6tcosh(2t)}
Use the property of Laplace transformation
L{e6tsinh(2t)e6tcosh(2t)}=L(e6tsinh(2t))L(e6tcosh(2t))
Use the property
L(eatsinh(bt))=b(sa)2b2  and  L(eatcosh(bt))=sa(sa)2b2
Step 2
Hence,
L(e6tsinh(2t))=2(s(6))222
=2(s+6)24
Hence, L(e6tsinh(2t))=2(s+6)24
And,
L(e6tcosh(2t))=s(6)(s(6))222
=s+6(s+6)24
Hence, L(e6(6t)cosh(2t))=s+6(s+6)24
Step 3
Hence,L{e6tsinh(2t)e6tcosh(2t)}=(2(s+6)24)s+6(s+6)24
=2s+6
Hence, L{e6tsinh(2t)e6tcosh(2t)}=2s+6
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