Question

what is the Laplace transform ot J(t)=H(t-7)8te6t? Your answer should be expressed as a function of s using the correcd syntax Laplace transform is F(s) What is the Laplace transform of 12 sinh(2t) Your answer should be expressed as a function of s using the correct syntax Laplace transform is F(s)

Answer 1

a) $L(H(t-7)8te^{6t})=8e^{-7s}L((t+7)e^{6(t+7)})$ which is

$L(H(t-7)8te^{6t})=8e^{42}e^{-7s}L((t+7)e^{6t})$

Which is $L(H(t-7)8te^{6t})=8e^{42}e^{-7s}\left(L(te^{6t})+7L(e^{6t}) \right )$

Which equals

42 -Ts

b)

Lisinh(2t)) = -22 ,7-4

And

sinh(20 )- 2,2-4

Which is

Lisinh(20/t) = tanh

So

L( 12 sinh(20/t) = 12 tanh