# Laplace Transform

This set of MATLAB Multiple Choice Questions & Answers (MCQs) focuses on “Laplace Transform”.

1. The default Laplace transform, of functions, computed by MATLAB is __________
a) Unilateral
b) Bilateral
c) Multipolar
d) Cannot be computed

2. The laplace transform of step function, u(t), can be calculated by using _____
a) syms t; laplace(t/t)
b) laplace(1)
c) laplace(t/t)
d) sym t; laplace(t/t)

3. How many time domain representations of the following signal is possibly stable?

`F(s)=2s+4/(s2+4s+3)…. Where s is the Laplacian frequency`

a) 2 for sigma>-1
b) 2 for sigma>-3
c) Only 1 for -3<sigma<-1
d) 1 for sigma<-1

4. The Transfer Function of an L.T.I. system is ___________
a) the impulse response with 0 initial conditions
b) the impulse response with some initial conditions
c) the ramp response with 0 initial conditions
d) the step response with 0 initial conditions

5. What will be the output of the following code?

`syms ‘-t’; laplace(4*(-t))`

a) Syntactical Error
b) The laplace transform of the time reversed ramp function.
c) -4/s2
d) Logical Error

6. What is the output of the following code?

`(z,p)=tf2zp(,[1,0])`

a) Error
b) z=0,p=0
c) z=0,p=1
d) z=1,p=0

7. The final value theorem is applicable if __________
a) Poles lie on right half of s plane
b) Poles lie on left half of s plane
c) Poles lie on the imaginary axis
d) Zeros lie on left half of s plane

8. What is the output of the following code?

`laplace[‘t^t’]`

a) A gamma function
b) Error due to []
c) Error due to ‘’
d) Cannot be determined

9. If f(t)=f1(t)+f2(t), the laplace transform of f(t) exists if f1(t) and f2(t) does not have the same R.O.C.
a) True
b) False

10. What is the output of the following code?

`[r,p,k]=residu(z,p);….. Assuming z and p are vectors of unequal length`

a) Returns the transfer function as partial fractions
b) Returns the transfer function variable
c) Returns an error
d) Cannot be determined

11. What is the output of the following code?

`(r,p,k)=residue(z,p);….. Assuming z and p are vectors of unequal length`

a) Returns the residue and poles for the partial fractions
b) Returns the zeros and poles
c) Returns a syntactical error
d) Cannot be determined

12. What is the default variable used to represent the laplace transform in the output?
a) s
b) z
c) S
d) p

13. A causal system is stable if the pole lies on the right half of the s-plane.
a) True
b) False

14. The laplace transform of the following function.

```f(t)= 3 when t=[0-5]
=  0 otherwise is….. L denotes Laplace Transform```

a) L{3u(t+3)-3u(t-5)}
b) L{3u[t+5]-u[t-5]}
c) L(3u(t)-3u(t-5))
d) L(u[t]-3u[t+5])

15. What will be the output of the following code?

`ilaplace(‘1/s’)`

a) Error
b) 1
c) u(t)
d) 0

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

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

23. The following output is defined for _______

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

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

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

25. 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)