Free Printable Formative Assessment I on Laplace Transform

1.

Find L [ sin 2 t ]

t\ge0

a)

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

b)

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

c)

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

d)

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

2.

L [ cos h 2 t ]

t\ge0

a)

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

b)

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

c)

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

d)

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

3.

$L\left[\ e^{-2t\ \ \ \ }\cos\ 2t\right]^{ }$

t\ge0

a)

$\frac{s}{\left(s+2\right)^2+4}$

b)

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

c)

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

d)

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

e)

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

4.

$L\left[\ e^{3t\ \ \ \ }\cos\ h\ 2t\right]^{ }$

t\ge0

a)

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

b)

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

c)

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

d)

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

5.

Find the Laplace transform of f(t)

a)

b)

c)

d)

6.

Find the Laplace Transform of f(t)

a)

b)

c)

d)

7.

Find the Laplace Transform of

a)

b)

c)

d)

8.

Find the Laplace Transform of

a)

b)

c)

d)

9.

Find the Laplace Transform of function f(t)

a)

b)

c)

d)

10.

Find the Laplace Transform of function f(t)

a)

b)

c)

d)

11.

Find the Laplace Transform of

a)

b)

c)

d)

12.

Define this property: $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$

a)

Linearity Property

b)

First Shifting Property

c)

Convolution Theorem

d)

Second Shifting Property

13.

Define this property: $L\left(f\left(a\ t\right)\right)=\frac{1}{a}F\left(\frac{s}{a}\right)$

a)

Linearity Property

b)

First Shifting Property

c)

Multiplication Theorem

d)

Change of scale Property

14.

Find $L\left(e^{3t}\left(t^3-3t^2+5t\right)\right)$

a)

$\frac{2}{\left(s-3\right)^4}-\left(\frac{3}{\left(\left(s-3\right)^3\right)}\right)+\frac{5}{\left(s-3\right)^2}$

b)

$\frac{6}{\left(s-3\right)^4}-\left(\frac{6}{\left(s-3\right)^3}\right)+\frac{5}{\left(s-3\right)^2}$

c)

$\frac{2}{\left(s-3\right)^3}-\left(\frac{3}{\left(s-3\right)^{\left(2\right)}}\right)+\frac{5}{s-3}$

d)

NONE OF THEM

15.

Let L [f(t)]= F(s) and $g\left(t\right)=e^{5t}f\left(t\right)$ , what is L [g(t)]= G(s)?

a)

$G\left(s\right)=F\left(s-5\right)$

b)

$G\left(s\right)=\left(-1\right)^5\frac{\text{d}^5F\left(s\right)}{\text{d}s^5}$

c)

$G\left(s\right)=F\left(s+5\right)$

d)

$G\left(s\right)=\left(-1\right)^4\frac{\text{d}^4F\left(s\right)}{\text{d}s^4}$

16.

Given $g\left(t\right)=t^3f\left(t\right)$ , what is G(s)?

a)

$G\left(s\right)=F\left(s-3\right)$

b)

$G\left(s\right)=\left(-1\right)^3\frac{\text{d}^3F\left(s\right)}{\text{d}s^3}$

c)

$G\left(s\right)=F\left(s+3\right)$

d)

$G\left(s\right)=\left(-1\right)^2\frac{\text{d}^2F\left(s\right)}{\text{d}s^2}$

17.

Given $g\left(t\right)=\frac{f\left(t\right)}{t}$ , what is G(s)?

a)

$G\left(s\right)=\int_s^{\infty}F\left(u\right)du$

b)

$G\left(s\right)=\left(-1\right)\frac{\text{d}F\left(s\right)}{\text{d}s}$

c)

$G\left(s\right)=\int_{\infty}^sF\left(u\right)du$

d)

$G\left(s\right)=^{\left(-1\right)^{-1}}\frac{\text{d}F\left(s\right)}{\text{d}s}$

18.

What is the formula for Laplace Second Order Derivative?

a)

$ℒ\left(𝑓′(𝑡)\right)=𝑠𝐹(𝑠)−𝑓(0)$

b)

$ℒ\left(𝑓"(𝑡)\right)=𝑠^2𝐹(𝑠)−𝑠𝑓\left(0\right)−𝑓′\left(0\right)$

c)

$ℒ\left(𝑓"(𝑡)\right)=𝑠^2𝐹(𝑠)−𝑓(0)$

19.

What is the formula for Laplace First Order Derivative?

a)

$ℒ\left(𝑓′(𝑡)\right)=𝑠𝐹(𝑠)−𝑓(0)$

b)

$ℒ\left(𝑓"(𝑡)\right)=𝑠^2𝐹(𝑠)−𝑠𝑓\left(0\right)−𝑓′\left(0\right)$

c)

$ℒ\left(𝑓′(𝑡)\right)=𝑠^2𝐹(𝑠)−𝑓(0)$

20.

Given $g\left(t\right)=\frac{f\left(t\right)}{t}$ , what is G(s)?

a)

$G\left(s\right)=\int_s^{\infty}F\left(u\right)du$

b)

$G\left(s\right)=\left(-1\right)\frac{\text{d}F\left(s\right)}{\text{d}s}$

c)

$G\left(s\right)=\int_{\infty}^sF\left(u\right)du$

d)

$G\left(s\right)=^{\left(-1\right)^{-1}}\frac{\text{d}F\left(s\right)}{\text{d}s}$

21.

Class of Student

a)

SE E&TC A

b)

SE E&TC B

c)

SE ELEX

22.

Name of the student

4 lines

23.

Roll number of student XX like 01 for single digit

4 lines

Formative Assessment I on Laplace Transform

Total questions: 23

Worksheet time: 27mins

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