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Laplace Transform of f(t)*u(t)

  • Thread starter JonForbes
  • Start date
  • #1
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Homework Statement



I need to know what the laplace transform is for f(t) * u(t)

More specifically, h(t) = cos(3t)*u(t)

Homework Equations



I know that f(t-to) * u(t-to) = e-tos * F(s)


The Attempt at a Solution



So, f(t) = cos(3t)

F(s) = s/(s2 + 9)

In the formula I gave in (2), I would then think that to = 0, because we just are multiplying f(t) by u(t - 0).

So H(s) = e-0*s * F(s)

H(S) = 1* F(s) = s/(s2 + 9)

I think this is right but could someone confirm this?

Thanks!
 

Answers and Replies

  • #2
H(s)=*L(cos(3t)(s))=s/(s^2+9)
because L(cos(omega*t)(s)=s/(s^2+omega^2) for real s and s/(s^2+a) for complex s
 
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