# Instrumentation Transducers Questions and Answers – Standard Test Signals

This set of Instrumentation Transducers Multiple Choice Questions & Answers (MCQs) focuses on “Standard Test Signals”.

1. Which of the following represents Laplace transform of ramp signal?
a) 1S3
b) 1S2
c) 1S
d) 1

Explanation: Ramp function is given as r (t) = t for all t >0. Its Laplace transform gives 1S2.
Laplace transform can be found by:
0r(t)e-stdt.

2. What does this function represents?

a) u (t)
b) u (t-2)
c) u (t+2)
d) u (-t)

Explanation: Given diagram represents a step function, which is shifted to right by two units and can write as u(t-2).

3. Laplace transform function f (t) is F(S), then how will you represent Laplace transform for differential of f (t)?
a) SF(S)
b) F(S)
c) S.F(S)
d) F’(S)

Explanation: This is obtained by time differential property of Laplace transform.

4. How will you obtain a given function from unit step signals?

```f (t) = 1 for -1≤t≤1
0 otherwise```

a) u (t) – u (t+2)
b) u (t+1) – u (t-1)
c) u (t+1) + u(t-1)
d) 2.u (t)

Explanation: Given expression cancels common region in two functions, and the remaining will be function of our interest. u(t+1) is step signal with one unit left shifted, and u(t-1) is step signal with one unit right shifted.
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5. How will you represent given function?

a) u (t)
b) eat.u(t)
c) e-at.u(t)
d) eat.r(t)

Explanation: Given function is a decreasing exponential with initial amplitude one, where u(t) represents step function. u(t) gives initial amplitude and negative power of exponential gives a negative slop to function.

6. Which of the following function is represented using a given condition?

```f (t) = 1 for t=0
0 otherwise```

a) Step function
b) Sine function
c) Ramp function
d) Impulse function

Explanation: Impulse signal has a value only at t=0 and has zero value otherwise. Unit impulse function will have amplitude one at time t=0.

7. What is the result of the expression f(t)= u (t+2) – u (t-3)?
a) f (t) = 1 for -2 ≤ t ≤ 3
b) f (t) = 1 for 2 ≤ t ≤ 3
c) f (t) = 1 for -2 ≤ t ≤ -1
d) f (t) = 1 for -2 ≤ t ≤ 0

Explanation: u (t) is step function, and subtracting two shifted step functions will cancel their common region and produces new function. u(t+2) is a step signal with two units shifted left side and u(t-3) is a step signal with three units shifted right side.

8. Transfer function of a system is given by 1/S. If system has a step input, what will be the output in time domain?(Function exist only for positive time value)
a) Step signal
b) Impulse signal
c) Sinusoidal signal
d) Ramp signal

Explanation: Transfer function is ratio of Output to Input and hence Output can be obtained as a product of transfer function and input, which gives 1/S2. For a positive sided signal using inverse Laplace transform, output is obtained as ramp signal.

9. Function f (t) has Laplace transform F(S). How will you represent Laplace transform of integral of f(t)?
a) S.F(S)
b) F(S)
c) F(S2)
d) F(S)S

Explanation: This is obtained by integration property of Laplace transform.

10. Which of the following represents Laplace transform of sinh(at)?
a) a(S2+a2)
b) a(S2-a2)
c) S(S2+a2)
d) S(S2-a2)

Explanation: Given function represents hyperbolic sine function. Hyperbolic sine function can be represented as sinhx= (ex-e-x)2. Applying Laplace transform equation to this expression, we obtain Laplace transform of hyperbolic sine function.

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