Find the partial fraction for ( 2 s − 8 ) ( s − 2 ) ( s − 3 ) \frac{\left(2s-8\right)}{\left(s-2\right)\left(s-3\right)} ( s − 2 ) ( s − 3 ) ( 2 s − 8 )

4 s − 2 − 2 s − 3 \frac{4}{s-2}-\frac{2}{s-3} s − 2 4 − s − 3 2

2 s − 2 − 4 s − 3 \frac{2}{s-2}-\frac{4}{s-3} s − 2 2 − s − 3 4

3 s − 2 − 2 s − 3 \frac{3}{s-2}-\frac{2}{s-3} s − 2 3 − s − 3 2

Find the Inverse Laplace for ( 2 s − 8 ) ( s − 2 ) ( s − 3 ) \frac{\left(2s-8\right)}{\left(s-2\right)\left(s-3\right)} ( s − 2 ) ( s − 3 ) ( 2 s − 8 )

4 e − 2 t − 2 e − 3 t 4e^{-2t}-2e^{-3t} 4 e − 2 t − 2 e − 3 t

2 e − 2 t − 4 e − 3 t 2e^{-2t}-4e^{-3t} 2 e − 2 t − 4 e − 3 t

e − 2 t − e − 3 t e^{-2t}-e^{-3t} e − 2 t − e − 3 t

3.2 Inverse Laplace Transform

Authored by SYAFAWATI HASBI

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Inverse Laplace transform, transform

$f\left(t\right)\ to\ F\left(s\right)$

$F\left(s\right)\ to\ f\left(t\right)$

$f'\left(t\ \right)\ to\ f\left(t\right)$

$f\left(t\right)\ to\ f'\left(t\right)$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find $L^{-1}\left(\frac{s}{s^2+25}\right)$

cos 25t

sin 5t

cos 5t

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find $L^{-1}\left(\frac{1}{s^2+1}\right)$

sin t

sin 5t

cos t

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L^{-1}\left(\frac{6}{\left(s\right)}-\frac{4s}{s^2+25}\right)$ What is the property use to find the Inverse Laplace Transform of this equation?

Second Shifting Property

First Shifting Property

Linearity Property

Convolution theorem

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L^{-1\ }\left(\frac{4s}{s^2+25}+\frac{2}{3\left(s^2+1\right)}\right)$

$4\ \cos\ 25t+\frac{2}{3}\sin\ t$

$\cos\ 5t+\ \sin\ t$

$4\ \cos\ 5t\ +\frac{2}{3}\sin\ t$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The $L^{-1}\left(\frac{4}{\left(s^2+9\right)}\right)$ is $a\ \sin\ 3t$ . What is a?

$\frac{2}{3}$

$\frac{4}{3}$

$3$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L\left(t^{\left(4\right)}\right)$ ?

$\frac{24}{s^5}$

$\frac{4}{s^5}$

$\frac{1}{s^5}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L^{-1}\left(\frac{24}{s^5}\right)$ is $t^4$ . What is $L^{-1}\left(\frac{1}{s^{\left(5\right)}}\right)$ ?

$\frac{24}{s^5}$

$\frac{1}{24}t^4$

$\frac{1}{24}t^5$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L^{-1}\left(\frac{4}{s^{\left(3\right)}}\right)$

$4t^3$

$2t^2$

$2t^3$

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$L^{-1}\left(\frac{3}{s^2+36}\right)$

$\frac{1}{2\ }\sin\ 6t$

$\frac{3}{5}\sin\ 5t$

$\cosh2t$

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3.2 Inverse Laplace Transform

Inverse Laplace transform, transform

Find L−1(ss2+25)L^{-1}\left(\frac{s}{s^2+25}\right)L−1(s2+25s​)

Find L−1(1s2+1)L^{-1}\left(\frac{1}{s^2+1}\right)L−1(s2+11​)

L−1(6(s)−4ss2+25)L^{-1}\left(\frac{6}{\left(s\right)}-\frac{4s}{s^2+25}\right)L−1((s)6​−s2+254s​) What is the property use to find the Inverse Laplace Transform of this equation?

L−1 (4ss2+25+23(s2+1))L^{-1\ }\left(\frac{4s}{s^2+25}+\frac{2}{3\left(s^2+1\right)}\right)L−1 (s2+254s​+3(s2+1)2​)

The L−1(4(s2+9))L^{-1}\left(\frac{4}{\left(s^2+9\right)}\right)L−1((s2+9)4​) is a sin⁡ 3ta\ \sin\ 3ta sin 3t . What is a?

L(t(4))L\left(t^{\left(4\right)}\right)L(t(4)) ?

L−1(24s5)L^{-1}\left(\frac{24}{s^5}\right)L−1(s524​) is t4t^4t4 . What is L−1(1s(5))L^{-1}\left(\frac{1}{s^{\left(5\right)}}\right)L−1(s(5)1​) ?

L−1(4s(3))L^{-1}\left(\frac{4}{s^{\left(3\right)}}\right)L−1(s(3)4​)

L−1(3s2+36)L^{-1}\left(\frac{3}{s^2+36}\right)L−1(s2+363​)

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Find $L^{-1}\left(\frac{s}{s^2+25}\right)$

Find $L^{-1}\left(\frac{1}{s^2+1}\right)$

$L^{-1}\left(\frac{6}{\left(s\right)}-\frac{4s}{s^2+25}\right)$ What is the property use to find the Inverse Laplace Transform of this equation?

$L^{-1\ }\left(\frac{4s}{s^2+25}+\frac{2}{3\left(s^2+1\right)}\right)$

The $L^{-1}\left(\frac{4}{\left(s^2+9\right)}\right)$ is $a\ \sin\ 3t$ . What is a?

$L\left(t^{\left(4\right)}\right)$ ?

$L^{-1}\left(\frac{24}{s^5}\right)$ is $t^4$ . What is $L^{-1}\left(\frac{1}{s^{\left(5\right)}}\right)$ ?

$L^{-1}\left(\frac{4}{s^{\left(3\right)}}\right)$

$L^{-1}\left(\frac{3}{s^2+36}\right)$