Find the laplace transform of this function. f(t)=e^{-2t}\sin 3t \sin t

vazelinahS 2021-09-16 Answered
Find the laplace transform of this function
f(t)=e2tsin3tsint
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Expert Answer

krolaniaN
Answered 2021-09-17 Author has 86 answers

f(t)=e2tsin3tsint
f(t)=e2tsin3tsint
f(t)=e2tsin3tsint
=e2t2[cos(3tt)cos(3t+t)]
=e2t2[cos2tcos4t]
[sinαsinβ=12[cos(αβ)cos(α+β)]]
L{f(t):s}=L{e2t2[cos2tcos4t]:s}
=12L{(cos2tcos4t):s+2}
[L{eatf(t):s}=L{f(t):s+a}]
=12[L{cos2t:s+2}L{cos4t:s+2}]
L[eax:s]=0eaxesxdx
=0e(sa)xdx
=[e(sa)x(sa)]0
=1sa  for  s>a
[limxe(sa)x=0]
so L{eiωx:s}=1siω
=s+iω(siω)(s+iω)
=s+iωs2+ω2

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