MATLAB Questions and Answers – Laplace Transform – 2

This set of MATLAB written test Questions & Answers focuses on “Laplace Transform – 2”.

1. An L.T.I. system is stable if _______
a) Poles lie on left half of s-plane
b) The R.O.C. encompasses the imaginary axis
c) The poles lie on the left half of s-plane and the R.O.C. encompasses the imaginary axis
d) Cannot be determined

Explanation: An L.T.I. system is stable if and only if both the conditions Poles lie on left half of s-plane and R.O.C. encompasses the imaginary axis are satisfied.

2. The final value of the following transfer function is ________

`F(s)= 2/s(s-824)`

a) Not calculable
b) -1/412
c) 0
d) 1

Explanation: We find that the pole of the given transfer function lies in the right half of s-plane. The system is not stable so we cannot apply the final value theorem and the final value is not calculable.

3. The number of inverse lapalace transform of a function is equal to ________
a) the number of poles
b) the number of poles+1
c) the number of poles-1
d) cannot be determined

Explanation: It is seen that the number of possible inverse laplace transform of any function is equal to the number of poles it has +1. Considering a function F(s)=A/s+1 + B/s+3=F1(s)+F2(s), the inverse laplace transform would exist if the inverse laplace transform is absolutely converging in a region. There are 3 regions that can have an absolutely converging state for F1(s) and F2(s) simultaneously and hence, only option the number of poles+1 is correct.

4. The laplace transform method used to solve a differential function is ____ than the classical way.
a) Easier
b) Harder
c) Moderately difficult
d) Relatively difficult

Explanation: The classical way is more tideous while the laplace transform allows it to represent the differential function in an algebraic form. Thereafter, the inverse laplace transform does the work.

5. What is the output of the following code?

`laplace[t,t,2]`

a) 1/16
b) Error
c) 1/s^2
d) Cannot be determined

Explanation: The input to the laplace command cannot be within []. Since the input is given within [], this will result in an error. The output would’ve been option 1/16 if the input was given within parentheses.

6. The laplace transform of a cascaded system is defined if _______
a) the individual systems have a common R.O.C.
b) the individual systems doesn’t have a common R.O.C.
c) the impulse response of each system is defined
d) cannot be determined

Explanation: It’s necessary for the individual systems, in a cascaded system, to have a common R.O.C.- otherwise the Laplace transform won’t be absolutely converging in a region. If ti doesn’t converge, the transform is not defined.

7. The inverse laplace transform of a function in s-domain is the transfer function of the system.
a) True
b) False

Explanation: The transfer function is an s-domain representation of the impulse response of a system. So, the inverse laplace transform of a function might generate the impulse response of a system but the transfer function is represented in s domain and so the above statement is false.

8. The following output is defined for _______

```>>ilaplace(1/s)
>> ans=
1```

a) t>0
b) t>=0
c) for all t
d) t<0

Explanation: The inverse laplace transform, in MATLAB, yields the time domain representation of the function for which the function is causal(t>=0). Hence, option t>=0 is correct only.

9. The differential equation d2p/dt2=9t has a solution.
a) 3/(2*t3)
b) cannot be determined
c) no solution
d) ilaplace(9/s4)

Explanation: It is not stated whether there are any initial conditions or not for the given differential equation. Hence, it’s not possible to state the solution of the above equation. If the initial conditions are 0, the laplace transform of the given equation yields- s2p(s)=9/s2 and a solution is reached by using option ilaplace(9/s4) in MATLAB and that solution is option 3/(2*t3). But we cannot talk about a solution until we know about the existence of the initial conditions.

10. What is the output of the following code?

`syms t; laplace(-t/t)`

a) The laplace transform of u(-t)
b) The laplace transform of -u(t)
c) The laplace transform of -u(-t)
d) The laplace transform of -u(t)

Explanation: The above command simply evaluated the laplace transform of -u(t) i.e. it’ll invert the step function due to the ‘-‘ sign but will evaluate the laplace transform for t>=0 only.

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