Question

Laplace transform of sin^3t is equal to​

Answer 1

Step-by-step explanation:

L

−1

(s+2)(s

2

+4s+9)

1

Let

f

(s)=

s+2

1

∴ f(s)=e

−2t

Let

g

(s)=

s

2

+4s+9

1

=

(s+2)

2

+5

1

=

5

1

(s+2)

2

+5

5

∴ g(s)=e

−2t

.

5

1

sin

5

t

By convolution,

∫.

−1

(s+2)(s

2

+4s+9)

1

=∫

0

t

e

−24

.

5

1

sin

54

.e

−2(t−u)

du

=

5

1

∫

0

t

sin

5

u.e

−2u

.e

−2t

.e

2u

du

=

5

1

.e

−2t

∫

0

t

sin

5

udu=

5

1

e

−2t

[

5

−(cos

5

t−cos0)

]

=

5

e

−2t

(1−cos

5

t)