Determine L^-1[F(s)] for the given F. F(s)=(s-2)/(s^2+2s+3)

Hello,

i'm here because i didn't found anything general on this topic, i need to know what is the expression of the laplace transform a composed function like that : $L\{f(x)\circ g(x)\}=L\{f(g(x))\}=??$

my complete equation to transform is : $$\begin{gathered} x(t)=4\times [\ddot{a}(t)cos(a(t))-\dot{a}(t{)}^{2}sin(a(t))]+2500 \\ y(t)=4\times [-\ddot{a}(t)sin(a(t))-\dot{a}(t{)}^{2}cos(a(t))]+\frac{3.711}{4}\times t^2+2700 \end{gathered}$$

the goal is to isolate the $a(t)$ function as a function of $x(t)$ and $y(x)$

Thanks for your time,

Robin Luiz

find the Laplace transform of f (t).
${\displaystyle f\left(t\right)=t\sin 3t}$

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Prove $F\left(s\right)=\frac{1}{s-2}\text{ then }f\left(t\right)$ is
a) $e^{2t}u\left(t\right)$
b) $u(t+2)$
c) $u(t-2)$
d) $e^{-2t}u\left(t\right)$

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${\displaystyle f\left(x\right)=12x^4+19x^3+9}$
f'(x)=

Inverse Laplace transformation

$(s^2+s)/(s^2+1)(s^2+2s+2)$

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