20094em3 Exercise 31

Engineering Mathematics 3

ITEGRAL TRASFORMS

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 Question 3.1.1 Find the laplace transform of the following: i. ii.

2

3⋅ t − 1

t   2

vii.

2

t + 3t + 1

viii. t⋅ ( t − 2)

sin

iii.

exp( − 2t)

iv.

cosh( 2⋅ t) −t

v.

e ⋅ sin( t)

vi.

t⋅ cos( t)

2

− 2t

e

xii.

− 2t

e

xiii.

sin( t) cosh( t)

−t

ix. x.

t ⋅e

xi.

cosh

t⋅ sin( 2t)

t   2

Section B Question 3.1.2 Find the laplace transform of i.

H ( t) =

t if 0 ≤ t < 2

v.

H ( t) =

( 1 − t) if t ≥ 2 ii.

H ( t) =

sin( t) if 0 ≤ t < π

H ( t) =

1 if 0 ≤ t < 1

vi.

F( t) =

H ( t) =

1 if 2 ≤ t 0 if 0 ≤ t < 1

1 if 0 ≤ t < 3 0 if t ≥ 3

vii.

G ( t) =

( −1) if 1 ≤ t < 2 iv.

if 0 ≤ t < 1

0 if 1 < t

0 if π ≤ t iii.

−t

e

( 2⋅ t) if 0 ≤ t < 1 t if t ≥ 1

viii. H( t) =

sin( t) if 0 ≤ t < π 0 if t ≥ π

1 if 1 ≤ t < 3 2 if 3 ≤ t

20094em3 Exercise 31.mcd

Copyright 2008 - 2009

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Engineering Mathematics 3

Question 3.1.3 i.

F( t) =

cos( t) if 0 ≤ t < π sin( t) if t ≥ π 2

ii.

G ( t ) = t ⋅ Φ ( t − 1)

iii.

H ( t) = e ⋅ Φ ( t − π )

iv.

F( t) =

−t

t if 0 ≤ t < 1 1 if 1 ≤ t < 2 ( − t) if t ≥ 2

20094em3 Exercise 31.mcd

Copyright 2008 - 2009

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