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QUESTION: 1

Determine the Laplace transform of given signal.

Q. x(t) = u( t - 2)

Solution:

QUESTION: 2

Determine the Laplace transform of given signal.

Q. x(t) = u( t + 2)

Solution:

QUESTION: 3

Determine the Laplace transform of given signal.

Q. x(t) = e^{-2t}u(t+1)

Solution:

Laplace transform e^{-at} u(t) = 1/s+a

for all Re(s) > - Re(a)

e^{-2t} u(t+1) = 1/(s+2)

QUESTION: 4

Determine the Laplace transform of given signal.

Q. x(t) = e^{2t}u(-t+2)

Solution:

QUESTION: 5

Determine the Laplace transform of given signal.

Q. x(t) = sin 5 t

Solution:

QUESTION: 6

Determine the Laplace transform of given signal.

Q. x( t) = u(t) - u(t - 2)

Solution:

QUESTION: 7

Determine the Laplace transform of given signal.

Q. x( t) = d/dt {te^{-1}u(t)}

Solution:

QUESTION: 8

Determine the Laplace transform of given signal.

Q. x( t) = tu(t)*cos2πt u(t)

Solution:

QUESTION: 9

Determine the Laplace transform of given signal.

Q. x( t) = t^{3}u(t)

Solution:

QUESTION: 10

Determine the Laplace transform of given signal.

Q. x(t) = u( t - 1) * e^{-2}^{t}u( t - 1)

Solution:

L{−e^{-at} u(t)}

= ∫(∞ to −∞) −e^{-at} u(t)e^{-st}dt

L{−e^{-at} u(t)}

= ∫(∞ to 0) − e^{-(s+a)t} dt

= - |e^{-(s+a)t}/−(s+a)|∞ to 0

= −1/s+a

=> L{−e^{-2t }u(t)} = -1/s+2

=> L{−e^{-2t }u(t-1)} = e^{-(s+2)}/s^{2 }…………(1)

q(t) = L{u(t-1)}

= e^{-s}/(s^{2})................(2)

Multiply (1) and (2)

= e^{-2(s+1)}/(s+2)

### Laplace Transform (Part - 1)

Video | 08:02 min

### Laplace Transform (Part -1)

Video | 53:44 min

### Laplace Transform (Part - 1)

Video | 08:02 min

### Laplace Transform (Part - 2)

Video | 07:35 min

- Test: Laplace Part - 1
Test | 10 questions | 30 min

- Test: Laplace Part - 2
Test | 10 questions | 30 min

- Test: Laplace Part - 3
Test | 10 questions | 30 min

- Laplace Transform - 1
Test | 10 questions | 30 min

- Laplace Transform - 2
Test | 10 questions | 30 min