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Worksheets

Laplace Transform

Total questions: 21

Worksheet time: 11mins

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11.

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

a)

cos 25t

b)

sin 5t

c)

cos 5t

12.

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

a)

sin t

b)

sin 5t

c)

cos t

13.

 L−1(6(s)−4ss2+25)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 (4ss2+25+23(s2+1))L^{-1\ }\left(\frac{4s}{s^2+25}+\frac{2}{3\left(s^2+1\right)}\right)  

a)

 4 cos⁡ 25t+23sin⁡ t4\ \cos\ 25t+\frac{2}{3}\sin\ t  

b)

 cos⁡ 5t+ sin⁡ t\cos\ 5t+\ \sin\ t  

c)

 4 cos⁡ 5t +23sin⁡ t4\ \cos\ 5t\ +\frac{2}{3}\sin\ t  

15.

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

a)

 24s5\frac{24}{s^5}  

b)

 4s5\frac{4}{s^5}  

c)

 1s5\frac{1}{s^5}  

16.

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

a)

 24s5\frac{24}{s^5}  

b)

 124t4\frac{1}{24}t^4  

c)

 124t5\frac{1}{24}t^5  

17.

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

a)

 4t34t^3  

b)

 2t22t^2  

c)

 2t32t^3  

18.

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

a)

 12 sin⁡ 6t\frac{1}{2\ }\sin\ 6t  

b)

 35sin⁡ 5t\frac{3}{5}\sin\ 5t  

c)

 cosh⁡2t\cosh2t  

19.

 L−1(F(s−5))=e5tf(t)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  aa   value?

a)

4

b)

5

c)

3

20.

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

a)

 e2tte^{2t}t  

b)

 ett2e^tt^2  

c)

 e3tte^{3t}t  

21.

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

a)

 e4t(cos⁡ 4t+sin⁡ 4t)e^{4t}\left(\cos\ 4t+\sin\ 4t\right)  

b)

 e2t(cos⁡ 2t+sin⁡ 2t)e^{2t}\left(\cos\ 2t+\sin\ 2t\right)  

c)

 e2t(4cos⁡ t+4sin⁡ t)e^{2t}\left(4\cos\ t+4\sin\ t\right)