Free Printable CIRCUIT ANALYSIS BY LAPLACE TRANSFORM

1.

Which one is the correct definition of Laplace transform?

a)

$F\left(s\right)=\int_0^{\infty}f\left(t\right)e^{st}dt$

b)

$F\left(s\right)=\int_0^{\infty}f\left(t\right)e^{-st}dt$

2.

Which F(s) can be used to describe a unilateral Laplace transform?

a)

$F\left(s\right)=\int_{-\infty}^{\infty}f\left(t\right)e^{-st}dt$

b)

$F\left(s\right)=\int_0^{\infty}f\left(t\right)e^{-st}dt$

3.

How to transform

f\left(t\right)=7

by using definition of integral

a)

$\int_0^{\infty}7e^{st}\ dt$

b)

$\int_0^1\ \ 7.e^{st}\ \ dt$

c)

$\int_0^{\infty}7e\ dt$

d)

$\int_0^{\infty\ \ }7e^{-st\ }dt$

4.

Find $L\left\{5u\left(t\right)\right\}$

a)

$\frac{1}{5s}$

b)

$\frac{5}{s}$

c)

$5s$

d)

$\frac{s}{5}$

5.

Find $L\left\{e^{-2t}\right\}$

a)

$\frac{2}{s+2}$

b)

$\frac{1}{s-2}$

c)

$\frac{1}{s+2}$

d)

$\frac{1}{s-1}$

6.

Find $L\left\{e^{4t}\right\}$

a)

$\frac{1}{s+4}$

b)

$\frac{1}{s-4}$

c)

$\frac{4}{s+1}$

d)

$\frac{4}{s-1}$

7.

Find $L\left\{\sin3t\right\}$

a)

$\frac{1}{s+3}$

b)

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

c)

$\frac{3}{s^2+9}$

d)

$\frac{3}{s^2-9}$

8.

Find $L\left\{\cos4t\right\}$

a)

$\frac{4}{s^2-16}$

b)

$\frac{4}{s^2+16}$

c)

$\frac{s}{s^2+16}$

d)

$\frac{s^2}{s^2-16}$

9.

Find $L\left\{2te^{-5t}\right\}$

a)

$\frac{1}{\left(s+5\right)^2}$

b)

$\frac{1}{\left(s-5\right)^2}$

c)

$\frac{2}{\left(s-5\right)^2}$

d)

$\frac{2}{\left(s+5\right)^2}$

10.

Find $L\left\{e^{3t}t\right\}$

a)

$\frac{1}{s^3}$

b)

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

c)

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

d)

$\frac{3}{s-1}$

11.

Find $L\left\{t^4\right\}$

a)

$\frac{24}{s^4}$

b)

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

c)

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

d)

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

12.

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

a)

$\frac{2}{3}u\left(t\right)$

b)

$\frac{2}{3}t$

c)

$\frac{3}{2}u\left(t\right)$

d)

$\frac{3}{2}t$

13.

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

a)

$3\cos2t$

b)

$3e^{2t}$

c)

$3t$

d)

$3e^{-2t}$

14.

Find $L^{-1}\left\{\frac{s}{s^2+4}\right\}$

a)

$\cos2t$

b)

$2\cos2t$

c)

$\sin2t$

d)

$2\sin2t$

15.

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

a)

$\frac{3}{2}e^{-t}\ +\ \frac{3}{2}e^{-3t}$

b)

$\frac{3}{2}e^t\ \ +\ \frac{3}{2}e^{3t}$

c)

$\frac{1}{2}e^{-t}\ \ +\ \ \frac{1}{2}e^{-3t}$

d)

$\frac{1}{2}e^t\ \ +\ \ \frac{1}{2}e^{3t}\ \$

16.

$L\left(e^{2t\ }\sin\ t\right)$ What is a and f(t)?

a)

$a=2,\ f\left(t\right)=e^{2t}$

b)

$a=4,\ f\left(t\right)=\cos\ t$

c)

$a=2,\ f\left(t\right)=\sin\ t$

17.

Determine the partial fraction for

F\left(s\right)=\frac{8s+38}{\left(2s-1\right)\left(s+3\right)}

a)

$\frac{6}{2s-1}+\frac{2}{s+3}$

b)

$\frac{-2}{s+3}+\frac{12}{2s-1}$

c)

$\frac{12}{2s-1}-\frac{2}{s+3}$

18.

Using table of Laplace Transform determine :

L\left\{e^{4t}-2t^4+\cos\ 8t\ -\ 1\right\}

a)

$F\left(s\right)=\frac{1}{s-4}-\frac{8}{s^5}+\frac{s}{s^2+64}-\frac{1}{s}$

b)

$F\left(s\right)=\frac{1}{s-4}-\frac{48}{s^5}+\frac{s}{s^2+64}-\frac{1}{s}$

c)

$F\left(s\right)=\frac{1}{s+4}-\frac{24}{s^5}+\frac{s}{s^2+64}-\frac{1}{s}$

19.

Transform

f\left(t\right)=e^{-2t}\cos\ 4t\ +\ e^{3t\ }\sin\ 6t

a)

$F\left(s\right)=\frac{s-2}{\left(s-2\right)^2+16}+\frac{s+3}{\left(s-3\right)^2+36}$

b)

$F\left(s\right)=\frac{s+2}{\left(s+2\right)^2+16}+\frac{s-3}{\left(s-3\right)^2+6}$

c)

$F\left(s\right)=\frac{s+2}{\left(s+2\right)^2+16}+\frac{s-3}{\left(s-3\right)^2+36}$

20.

Find inverse of

F\left(s\right)=\frac{1}{\left(s+1\right)\left(s-1\right)}

a)

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

b)

$\frac{-2}{s+1}+\frac{2}{s-1}$

c)

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

CIRCUIT ANALYSIS BY LAPLACE TRANSFORM

Total questions: 20

Worksheet time: 1hrs 10mins

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