20094em3 Exercise 32

Engineering Mathematics 3

ITEGRAL TRASFORMS

Inverse Laplace Transforms Grade 50% off the total score within the first week after due date. Zero score after the first week. Name : Group: Subject: Topic: Date Due: Date of Submission:

Section A (Table) Question 3.2.1 Use the laplace transform to find the following 1 i.

3

1

,s > 0

vi.

2s + 3

s

ii.

1 1

s−

iii.

,s >

1

,s > 0

s 2

, s > 3

s −9

, s > −1

2

, s > −1

,s > 0

2

2

x.

s− 1

1

,s > 3

iv.

g( s) =

( s − 1) − 4 ii.

1

g( s) =

2

2

s +9

, s > −2

g( s) =

s⋅ ( s + 1)

s

ix.

3

1

3

s +9

,s > 2

3

1

2s + 2 Question 3.2.2 Find G(t). i.

2

viii.

1

( s + 2)

v.

vii.

2

( s − 2)

iv.

1

,s > −

,s > 0

v.

g( s) =

( s − 1) + 4

1 s

−

1 2

+

s

3

,s > 0

s

1 ( 2s − 3)

1

3

,s >

3 2

− 2s

iii.

g( s) =

e

s

,s > 0

20094em3 Exercise 32.mcd

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Engineering Mathematics 3

Section B (Use Partial Fractions) Question 3.2.3 Find H(t). i.

h ( s) =

1 s⋅ ( s − 1)

iii. iv.

h ( s) =

h ( s) =

h ( s) =

2⋅ s

, s > −2

2

s + 5⋅ s + 6

s

, s>

s⋅ ( 2s − 1) 1

h ( s) =

v.

1

1+

ii.

, s > 1

vi.

1

s ⋅ ( s − 2) 1

(

2

( s + 1) ⋅ s + 1

)

3s + 1 2

, s > −2

s + 4s + 4

2

1

, s>2

2

h ( s) =

vii.

h ( s) =

( s − 2)

2

s⋅ ( s + 1)

,s > 0

, s > −1

Section C (Use Completing of squares) Section 3.2.4 Find G(t). i.

s

g( s) =

2

s + 5⋅ S + 6

ii.

2s − 1

g( s) =

2

s + 5s + 6

iii.

1 − 3s

g( s) =

2

( s − 1) + 4

iv.

3s − 1

g( s) =

2

( s + 1) − 1

v.

2s − 1

g( s) =

2

( 2s − 1) + 4

Section D (Heaviside Theorem) Question 3.2.5. − 2s

Find G(t). if g( s) = e

1

⋅

where s > 0.

2

s +1 i.

− 2s

g( s) = e

⋅

1 2

, s > 0

s +1 Ans: G( t) = U( t − 2) ⋅ sin( t − 2) − 2s

ii.

g( s) =

( s + 1) ⋅ e 2

where s > 1.

( s + 1) − 4 1 1  Ans: G( t) = Φ ( t − 2) ⋅  ⋅ exp( − 3⋅ t + 6) + ⋅ exp( t − 2)  2 2  

20094em3 Exercise 32.mcd

Copyright 2008 - 2009

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