This set of Engineering Mathematics Questions and Answers for Campus interviews focuses on “Laplace Transform By Properties – 2”.

1. Transfer function may be defined as

a) Ratio of out to input

b) Ratio of laplace transform of output to input

c) Ratio of laplace transform of output to input with zero initial conditions

d) None of the above

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Explanation: Transfer function may be defined as the ratio of laplace transform of output to input with zero initial conditions.

2. Poles of any transfer function is define as the roots of equation of denominator of transfer function.

a) True

b) False

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Explanation: Let transfer function be defined as G(s)/H(s), then poles of transfer function may be defined as H(s)=0.

3. Zeros of any transfer function is define as the roots of equation of numerator of transfer function.

a) True

b) False

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Explanation: Let transfer function be defined as G(s)/H(s), then zeros of transfer function may be defined as G(s)=0.

4. Find the poles of transfer function which is defined by input x(t)=5Sin(t)-u(t) and output y(t)=Cos(t)-u(t).

a) 4.79, 0.208

b) 5.73, 0.31

c) 5.89, 0.208

d) 5.49, 0.308

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Explanation: Given ,y(t) =Cos(t) – u(t) and x(t) = 5Sin(t) – u(t),

Roots of equation s^{2} – 5s + 1 = 0 is s = 4.79, 0.208.

5. Find the equation of transfer function which is defined by y(t)-∫_{0}^{t} y(t)dt + ^{d}⁄_{dt} x(t) – 5Sin(t) = 0

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6. Find the poles of transfer function given by system ^{d2}⁄_{dt2} y(t) – ^{d}⁄_{dt} y(t) + y(t) – ∫_{0}^{t} x(t)dt = x(t)

a) 0, 0.7 ± 0.466

b) 0, 2.5 ± 0.866

c) 0, 0 .5 ± 0.866

d) 0, 1.5 ± 0.876

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7. Find the transfer function of a system given by equation ^{d2}⁄_{dt2} y(t-a) + x(t) + 5 ^{d}⁄_{dt} y(t) = x(t-a).

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

b)(e^{-as}-5s)/(e^{-as} s^{2})

c) (e^{-as}-s)/(2+e^{-as} s^{2})

d) (e^{-as}-5s)/(1+e^{-as} s^{2})

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Explanation: Given,

^{d2}⁄

_{dt2}y(t-a) + x(t) + 5

^{d}⁄

_{dt}y(t) = x(t-a).

Taking laplace transform, s^{2} Y(s) e^{-sa} + X(s) + 5sY(s) = e^{-as} X(s)

Hence, H(s) = ^{Y(s)}⁄_{X(s)} =(e^{-as}-5s)/(1+e^{-as} s^{2}).

8. Any system is said to be stable if and only if

a) It poles lies at the left of imaginary axis

b) It zeros lies at the left of imaginary axis

c) It poles lies at the right of imaginary axis

d) It zeros lies at the right of imaginary axis

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Explanation: Any system is said to be stable if and only if it poles lies at the left of imaginary axis.

9. The system given by equation 5 ^{d3}⁄_{dt3} y(t) + 10 ^{d}⁄_{dt} y(t) – 5y(t) = x(t) + ∫_{0}^{t} x(t)dt, is

a) Stable

b) Unstable

c) Has poles 0, 0.455, -0.236±1.567

d) Has zeros 0, 0.455, -0.226±1.467

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10. Find the laplace transform of input x(t) if the system given by ^{d3}⁄_{dt3} y(t) – 2 ^{d2}⁄_{dt2} y(t) –^{d}⁄_{dt} y(t) + 2y(t) = x(t), is stable.

a) s + 1

b) s – 1

c) s + 2

d) s – 2

View Answer

Explanation:

^{d3}⁄

_{dt3}y(t) – 2

^{d2}⁄

_{dt2}y(t) –

^{d}⁄

_{dt}y(t) + 2y(t) = x(t),

Taking laplae transform,

(s^{3} – 2s^{2} – s + 2)Y(s) = X(s)

H(s) = ^{Y(s)}⁄_{X(s)} = ^{1}⁄_{(s-1)(s+1)(s+2)}

For the system to be stable, X(s) = s – 1.

11. The system given by equation y(t – 2a) – 3y(t – a) + 2y(t) = x(t – a),is

a)Stable

b)Unstable

c) Marginally stable

d) 0

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**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

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