Free Printable Laplace Transform

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Worksheets

Laplace Transform

Total questions: 21

Worksheet time: 11mins

Name

Class

Date

1.

a)

b)

c)

d)

2.

a)

b)

c)

d)

3.

a)

b)

c)

d)

4.

a)

b)

c)

d)

5.

a)

b)

c)

d)

6.

a)

b)

c)

d)

7.

a)

b)

c)

d)

8.

a)

b)

c)

d)

9.

a)

b)

c)

d)

10.

a)

b)

c)

d)

11.

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

a)

cos 25t

b)

sin 5t

c)

cos 5t

12.

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

a)

sin t

b)

sin 5t

c)

cos t

13.

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

a)

Second Shifting Property

b)

First Shifting Property

c)

Linearity Property

d)

Convolution theorem

14.

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

a)

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

b)

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

c)

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

15.

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

a)

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

b)

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

c)

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

16.

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

a)

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

b)

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

c)

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

17.

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

a)

$4t^3$

b)

$2t^2$

c)

$2t^3$

18.

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

a)

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

b)

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

c)

$\cosh2t$

19.

$L^{-1}\left(F\left(s-5\right)\right)=e^{5t}f\left(t\right)$ Based on first shifting property for Inverse Laplace transform, what is $a$ value?

a)

4

b)

5

c)

3

20.

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

a)

$e^{2t}t$

b)

$e^tt^2$

c)

$e^{3t}t$

21.

$L^{-1}\left(\frac{s}{\left(s-4\right)^2+16}\right)$

a)

$e^{4t}\left(\cos\ 4t+\sin\ 4t\right)$

b)

$e^{2t}\left(\cos\ 2t+\sin\ 2t\right)$

c)

$e^{2t}\left(4\cos\ t+4\sin\ t\right)$

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