# Tagged Questions

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### Fourier transform of a Laplace transform

Is there an easy way to find the Fourier transform of a Laplace transform of function? $$F[L[f(t)]_{s}]$$ Where my $f(t)$ is $\sqrt{t}$. However, Before finding the Fourier transform I do the ...
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Find the inverse Laplace transform of the giveb function by using the convolution theorem. $$F(x) = \frac{s}{(s+1)(s^2+4)}$$ If I use partial fractions I get: $$\frac{s+4}{5(s^2+4)} - ... 1answer 179 views ### Laplace transform having this unusual property in convolution? Here is the problem Solve y'(t) = 1 - \int_{0}^{t} y(t - v)e^{-2v}dv The solution sets \mathcal{L}(y) = Y(s) and does the following Notice that in step 1, they have$$Y(s)\dfrac{1}{s+2} ...
Let $\mathcal {L}^{-1}[\cdot]$ be an inverse Laplace transform. Let $A$ be a square matrix, and $I$ an identity matrix. Based on the fact that $\mathcal {L} ^{-1} [{(sI-A)}^{-1}] = e ^{tA}$, how can ...
$2y''+y'+2y=\delta(t-5)$ $y(0)=0, y'(0)=0$ Consider the system given by ODE above in which an oscillation is excited by a unit impulse at $t=5$. Suppose that it is desired to bring the system to ...