find the Laplace transform of f (t) . f(t)=te^{2t} \cos 3t

sodni3

sodni3

Answered question

2021-09-13

find the Laplace transform of f (t)
f(t)=te2tcos3t

Answer & Explanation

rogreenhoxa8

rogreenhoxa8

Skilled2021-09-14Added 109 answers

Step 1
Given f(t)=te2tcos3t
Since L(cosat)=ss2+a2
L(cos3t)=3s2+32=3s2+9
Multiplication by t property given
L(tf(t))=(1)dds[F(s)]
L(tcos3t)=1dds[3s2+9]
=3dds[(s2+9)1]
=3(1)(s2+a)11dds(s2+9)
=3(s2+9)2(2s)=6s(s2+9)2
First shiffting theorem gives
L(eatf(t))=F(sa)
L(e2ttcos3t)=6(s2)((s2)2+9)2
=6(s2)(s2+44s+9)2
=6(s2)(s24s+13)2

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