Mathematics, 14.07.2019 12:00 john9727
Find the inverse laplace transform f(t)=l−1{f(s)} of f(s)=2s+8/s2+13s> 0
Answers: 1
![f(s)=2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}\\ \\ \text{Now take inverse Laplace Transform on both the sides we get}\\ \\ L^{-1}[f(s)]=L^{-1}[2*\frac{s}{s^2+13}+8*\frac{1}{s^2+13}]\\ \\ L^{-1}[f(s)]=2*L^{-1}\frac{s}{s^2+13}+8*L^{-1}\frac{1}{s^2+13}\\ \\ \text{From the Laplace inverse transform table we can re-write above equation as }\\ \\ f(t)=2cos\sqrt{13}t+ \frac{Sin\sqrt{13}t}{\sqrt{13}} \\](/tpl/images/0088/5302/78355.png)
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