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QUESTION: 1

Consider the function f(t) having Laplace transform,the final value of f(t) would be

Solution:

L^{-1}[F(S)] = sin ω_{0}t

f(t) - sin ω_{0}t

So, - 1 __<__ f(∞) __<__1

QUESTION: 2

The transfer function H(S) of a stable system is

the impulse response is

Solution:

System is stable

⇒

QUESTION: 3

If L[f(t)] = then f(0^{+}) and f(∞) are given by

Solution:

QUESTION: 4

Find the laplace transform of time function shown in figure.

Solution:

Taking laplace,

QUESTION: 5

Consider the following signal:

the laplace transform of above system is

Solution:

QUESTION: 6

Consider a signal x(t) having laplace transform given by,

The time domain signal x(t) is equal to

Solution:

QUESTION: 7

Given that:

then, L[h(t)] is

Solution:

Convolution in time domain is multiplication in s-domain.

∴

QUESTION: 8

A causal LTI system is described by the difference equation, 2y[n] = αy[n- 2] - 2x[n] + βx[n - 1]. The system is stable only if,

Solution:

Taking z-transform

For system to bs stable, β can be of any value.

⇒

For system to be stable all poles should be inside unity circle.

QUESTION: 9

Match List-I (Function in time domain) with List-II (Corresponding Laplace Transform F(S)) and select the correct answer using the codes given below the lists:

List-I

A.

B.

C.

D.

List-II

1.

2.

3.

4.

Codes:

Solution:

QUESTION: 10

The lapiace transform of

Solution:

### Laplace Transform - 2

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### Laplace Transform (Part - 2)

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### Laplace Transform (Part - 2)

Video | 07:35 min

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