EE 402 ADVANCED MATHEMATICS FOR EE
t, 0 < t < 4
5, t > 4
1. Find the Laplace Transform of H(t), where H(t) =
A.
+
+
B. +
C.
+
+
−
D. +
−
2. The Laplace Transform of i(t) is given by I(s) =
A. 0
C. 2
B. 1
D. ∞
. At t → ∞, the value of i(t) tends to
(
)
3. The Laplace Transform is an operation that transforms a function __________ to a function of
__________.
A. time domain; frequency domain
C. frequency domain; time domain
B. continuous; discrete
D. discrete; continuous
4. Find the Laplace Transform of the equation with the given boundary conditions.
f"(t) + f(t) = sin (βt), f′(0) = 0, f(0) = 0
A. F(s) =
C. F(s) =
B. F(s) =
D. F(s) =
5. Find the Laplace Transform of e
f(t)
( )
A. F(s)e
C.
B. F(s + a)
D. F(s − a)
6. Find the Laplace Transform of e
A. Convolution
B. Time scaling
7. Let H(s) =
(
+a
f(t)
C. Conjugation
D. Translation
)
, ind h(t).
A. (e − 1)
C. (e
B. (e
D. (e + 1)
+ 1)
− 1)
8. Find the Laplace Transform of ℒ{t(t − 2)(t + 2)}.
A.
B.
!
!
−
+
!
!
C.
D.
!
!
−
+
!
!
9. Laplace Transform of F(s) = t + 2t + 3 is
A. f(t) = + +
C. f(t) = −
B. f(t) =
10.
+
+
−
−
−
−
D. f(t) = −
Find the Laplace Transform of ℒ
(
)
.
A. tcos(t) − 1
C. tcos(t) − 2
B. t + cos(t) − 1
D. t − sin (t) − 1
11.
Which of the following theorem best describes the linearity of Laplace Transform?
A. ℒ{af(t) + bg(t)} = aℒ{f(t)} + bℒ{g(t)} C.ℒ{f } = s − s f(0) − s f′(0) − ⋯ f
(0)
B. ℒ{e f(t)} = F(s − a)
D. ℒ ∫ f(τ)dτ = F(s)
12.
For a given function, it is found that f(−t) = f(t). What type of symmetry does f(t)
have?
A. odd symmetry
C. rotational symmetry
B. quarter-wave symmetry
13.
If f(x) = x + cos(x), then f(x) is
A. even function
B. constant function
D. even symmetry
C. odd function
D. neither even nor odd
14.
It is the power to which the highest order derivative is raised when the differential
coef icients are free from radicals and fractions.
A. degree
C. order
B. exponent
D. root
15.
A solution of differential equation containing a number of arbitrary constants equal
to the order of the equation.
A. particular solution
C. singular solution
B. general solution
D. integral solution
16.
In a series RLC circuit, the charge equation is described as Q" + Q′ + 14Q = 0.5sint(t).
Assuming no initial charge on the capacitor, but an initial current of 1 Ampere at t = 0 when
the voltage is irst applied, ind the steady state charge on the capacitor.
Hint: Steady state charge is the particular solution
A.
sin (t) +
cos (t)
C.
sin(t) −
cos (t)
B. −
sin (t) +
cos (t)
D. −
sin(t) −
cos (t)
17.
The equation
+
+
i = 0 represents a current i lowing in an electrical circuit
containing resistance R, inductance L and capacitance C connected in series. If R = 200Ω,
L= 0.20H and C = 20 x 10-6F, solve the equation for I given the boundary conditions that
when t = 0, i = 0 and di = 100.
A. i = 100te
C. i = 50te
B. i = 10te
D. i = 5te
18.
An RLC circuit connected in series has R = 10Ω, C = 10-2F, L = 0.5H, and an applied
voltage E = 12 volts. Assuming no initial current and no initial charge at t = 0 when the
voltage is irst applied, ind the subsequent current in the system.
A. i = e
sin (10t)
C. i = − e
cos (10t)
B. i =
e
cos (10t)
D. i = −
e
sin (10t)
19.
A ____________ is an expansion of a periodic function f(x) in terms of an in inite sum of
sines and cosines.
A. Gibb series
C. McLaurin series
B. Taylor series
D. Fourier series
20.
A 10Ω resistance and a 0.001F capacitance C are in series. An AC voltage e =
100sin(60t) is applied across the series circuit. Solve for the complimentary and particular
solution.
21.
A series circuit has R = 10Ω, L = 0.1H and C = 0.01F. An AC voltage e = 100cos(60t)
is applied across the series circuit. Solve for the complimentary and particular solution.
22.
A series RC circuit with R = 30Ω and C = 250μF is connected across an AC voltage
source of emf 100cos(100t) through a switch. The switch is closed at t = 0. Determine the
current when t = 0.01 second. Assume at t = 0, voltage across the capacitor is zero.
23.
A 10-ohm resistance R and a 1.0-henry inductance L are connected in series. An AC
voltage e = 100sin(60t) is applied across the series circuit. Solve for the particular solution
and complimentary solution.
24.
Determine the Laplace Transform of f(t) = e
sin(3t) cos (2t).