Find laplace transform of the following functions. f(t)=t \sin h(2t)

Kye 2021-09-15 Answered
Find laplace transform of the following functions
f(t)=tsinh(2t)
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Expert Answer

avortarF
Answered 2021-09-16 Author has 113 answers

Step 1
The given function is in the form of f(t)=tkg(t). The Laplace transform of tkg(t)  is  (1)kdkdskL[g(t)] that is L[tkg(t)]=(1)kdkdsk(L[g(t)])
Compare the function f(t)=tsinh(2t) with the f(t)=tkg(t) we found,
k=1
g(t)=sinh(2t)
Since, L[tkg(t)]=(1)kdkdsk(L[g(t)]) therefore L[tsinh2t]=(1)1dds(L[sinh2t])s˙(1)
Step 2
Since L[sinh(at)]=as2a2 , So use this find L[sinh(2t)]
L[sinh(2t)]=2s222
=2s24s˙(2)
From (1) and (2) , L[tsin(2t)]=dds[2s24].

Calculate dds[2s24]
dds[2s24]=2(s24)22s
=4s(s24)2
Therefore

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