Find the inverse Laplace transform of: $$\frac{2s}{(s+1{)}^{2}+4}$$

Baqling
2022-09-11
Answered

Find the inverse Laplace transform of: $$\frac{2s}{(s+1{)}^{2}+4}$$

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asked 2021-02-09

Transform:

$f\left(t\right)={\mathrm{cos}}^{2}at$

asked 2021-11-13

Use implicit differentiation to find ∂z / ∂x and ∂z / ∂y.

${x}^{2}-{y}^{2}+{z}^{2}-2z=4$

asked 2022-09-09

Laplace transform using 2nd shifting Theorem. $$\mathcal{L}(U(t-5){e}^{t-5})$$

a = 5, Therefore, $f(t-5)={e}^{t-5}$

since $\mathcal{L}(f(t))=F(s)$

$f(t)={e}^{t}$

and $\mathcal{L}(f(t))=\frac{1}{s-1}$

Therefore the answer is ${e}^{-5s}\frac{1}{s-1}$

It`s correct answer?

a = 5, Therefore, $f(t-5)={e}^{t-5}$

since $\mathcal{L}(f(t))=F(s)$

$f(t)={e}^{t}$

and $\mathcal{L}(f(t))=\frac{1}{s-1}$

Therefore the answer is ${e}^{-5s}\frac{1}{s-1}$

It`s correct answer?

asked 2022-03-31

I am having trouble finding the inverse Laplace transform of:

$\frac{1}{{s}^{2}-9s+20}$

I tried writing it in a different way:

$L}^{-1}\left\{\frac{1}{{(s-\frac{9}{2})}^{2}-{\left(\frac{1}{2}\right)}^{2}}\right\}=2{L}^{-1}\left\{\frac{\frac{1}{2}}{{(s-\frac{9}{2})}^{2}-{\left(\frac{1}{2}\right)}^{2}}\right\$

I tried writing it in a different way:

asked 2021-09-24

Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace tranform of the function below.

$(1+{e}^{-4t})}^{2$

asked 2022-09-26

How to calculate inverse Laplace transform of $\frac{7{s}^{2}+3s+5}{({s}^{2}-4s+29)({s}^{2}+25)}$?

asked 2022-09-14

Why following equality is satisfied

$$\mathcal{L}\left[\mathrm{exp}\left({\int}_{0}^{t}ds\frac{\dot{x}(s)}{x(s)}\right)\right]=\frac{1}{u-\frac{\mathcal{L}\left[\dot{x}\right](u)}{\mathcal{L}[x](u)}},$$

where $\mathcal{L}[\cdot ]$ denotes Laplace transform. Is this equation fulfilled for all x(t), and how one can derive it?

$$\mathcal{L}\left[\mathrm{exp}\left({\int}_{0}^{t}ds\frac{\dot{x}(s)}{x(s)}\right)\right]=\frac{1}{u-\frac{\mathcal{L}\left[\dot{x}\right](u)}{\mathcal{L}[x](u)}},$$

where $\mathcal{L}[\cdot ]$ denotes Laplace transform. Is this equation fulfilled for all x(t), and how one can derive it?