Compute the Inverse Laplace Transform of \(F(s) =\frac{s}{R^2s^2+16\pi^2}\)

take \(R=70\)

Your answer

asked 2021-01-31

Compute the Inverse Laplace Transform of \(F(s) =\frac{s}{R^2s^2+16\pi^2}\)

take \(R=70\)

asked 2021-05-12

One property of Laplace transform can be expressed in terms of the inverse Laplace transform as \(L^{-1}\left\{\frac{d^nF}{ds^n}\right\}(t)=(-t)^n f(t)\) where \(f=L^{-1}\left\{F\right\}\). Use this equation to compute \(L^{-1}\left\{F\right\}\)

\(F(s)=\arctan \frac{23}{s}\)

\(F(s)=\arctan \frac{23}{s}\)

asked 2020-11-08

asked 2021-02-16

\(y"+\omega^{2}y=\sin \gamma t , y(0)=0,y'(0)=0\)

1) \(y(t)=L^{-1}\bigg(\frac{\gamma}{(s^{2}+\omega^{2})^{2}}\bigg)\)

2) \(y(t)=L^{-1}\bigg(\frac{\gamma}{s^{2}+\omega^{2}}\bigg)\)

3) \(y(t)=L^{-1}\bigg(\frac{\gamma}{(s^{2}+\gamma^{2})^{2}}\bigg)\)

4) \( y(t)=L^{-1}\bigg(\frac{\gamma}{(s^{2}+\gamma^{2})(s^{2}+\omega^{2})}\bigg)\)

asked 2021-02-04

Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.

a) \(F(s)=\frac{3e^{-2s}}{s(s+3)}\)

b) \(F(s)=\frac{e^{-2s}}{s(s+1)}\)

c) \(F(s)=\frac{e^{-2s}-e^{-3s}}{2}\)

a) \(F(s)=\frac{3e^{-2s}}{s(s+3)}\)

b) \(F(s)=\frac{e^{-2s}}{s(s+1)}\)

c) \(F(s)=\frac{e^{-2s}-e^{-3s}}{2}\)

asked 2020-11-05

Find the inverse laplace transform of the function

\(Y(s)=\frac{e^{-s}}{s(2s-1)}\)

\(Y(s)=\frac{e^{-s}}{s(2s-1)}\)

asked 2020-11-07

Write down the qualitative form of the inverse Laplace transform of the following function. For each question first write down the poles of the function , X(s)

a) \(X(s)=\frac{s+1}{(s+2)(s^2+2s+2)(s^2+4)}\)

b) \(X(s)=\frac{1}{(2s^2+8s+20)(s^2+2s+2)(s+8)}\)

c) \(X(s)=\frac{1}{s^2(s^2+2s+5)(s+3)}\)

a) \(X(s)=\frac{s+1}{(s+2)(s^2+2s+2)(s^2+4)}\)

b) \(X(s)=\frac{1}{(2s^2+8s+20)(s^2+2s+2)(s+8)}\)

c) \(X(s)=\frac{1}{s^2(s^2+2s+5)(s+3)}\)

asked 2021-05-26

Find the indicated derivatives.

\(\displaystyle{r}={s}^{{{3}}}-{2}{s}^{{{2}}}+{3}\)

\(\displaystyle{r}={s}^{{{3}}}-{2}{s}^{{{2}}}+{3}\)

asked 2021-03-05

Find the indicated derivatives. \(\displaystyle{\frac{{{d}{r}}}{{{d}{s}}}}{\quad\text{if}\quad}{r}={s}^{{{3}}}-{2}{s}^{{{2}}}+{3}\)

asked 2020-12-25

which of the laplace transform is

\(1.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s-3}\)

\(2.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s-3}\)

\(3.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s+3}\)

\(4.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s+3}\)