APSC 246 System Dynamics
Quiz No. 1
Oct. 1-5, 2012
Student Name/ID:
Question (20 points total)
For a linear time-invariant system with input x(t) and output y(t)
(1).
If input is and the output is
1, what is the impulse
response of the system? (4 poin
APSC 246 System Dynamics
Quiz No. 3
Nov.26-30, 2012
Student Name/ID:
Question (5 points total)
9
, 0 0, 0 0
(1) What is the transfer function of the system?
(2) What is the impulse response of the system?
(3) If
sin , obtain the solution wi
APSC 246 System Dynamics
Quiz No. 2
Nov. 19-23, 2012
Student Name/ID:
Question (25 points total)
4 4
, 0 1, 0 1
2
(1) Obtain general solution of the following 2nd-order ODE using either method
of undetermined coefficients or variation of parameter.
APSC246 Solutions to Assignment #4 2012
Problem 1 (5 points) Verify if the given functions are solutions of the given differential
equation.
2 9 sin 2
, given functions:
sin
,
3 sin
,
Solution:
: 2 sin
cos
9 sin 2
. So No, it is not a s
APSC246 Solution to Assignment #1 2012
Problem 1: (10 points) For the signal x(t) illustrated below,
Sketch the signals.
(a) x(-t)
x(-t)
-12
0
-15
-24
0.5
-6
t
-1
(b) x(t+6)
x(t+6)
0.5
0
6
9
5
8
18
t
-1
(c) x(3t)
x(3t)
0.5
2
0
t
-1
@Dr. Yang Cao
Page 1
AP
APSC246-Solutions to Assignment 10 2012
Problem 1 (10 points) As we learned in Class, one of the LTI system properties is that if the
system input is , then assuming zero initial conditions, the system output is
, where is the systems impulse response.
F
APSC246 Solutions to Assignment #5 2011
Problem 1 (20 points) ( Find a general solution. Show the steps of derivation.
(a)
(b)
Solution:
, 0
, 0, 0
4
Let , or , then .
4 ln
8 ln
, !
8 ln
*
(b)
Let , or
So
" # " # " #
APSC246-Assignment 3 (Due 4:00PM, Oct. 5)
Problem 1: (10 points) Sketch the following signals:
(a)
(b)
(c)
(d)
5 7
5 7
2 1 2
4 2 4
where is the unit step function.
Problem 2: (5 points) Find proper mathematical expressions for the following piece-w
APSC246 Solutions to Assignment #2 2012
Problem 1: (10 points) Simplify the following expressions:
(a) cos 3
(b)
(c)
(d)
(Hint: Use LHopitals rule)
41
cos ! 5 !
3!
Solution:
(a) cos 3 # cos 3
(b)
$%
# cos #
(Hint: Use LHopitals rule)
si
APSC246-Solutions to Assignment #7 2012
Problem 1 (15 points) Which of the following sets of functions are linear dependent (LD)and
which are linear independent (LI)?
(a) sin 2 cos , sin 2 cos , 2sin cos , 2 sin cos
(Ans: LI)
(b) 1 2, 2 3 , 3 4 , 4 5
(
APSC246-Assignment 7 (Due 4:00PM November7) 2012
Problem 1 (15 points) Which of the following sets of functions are linear dependent (LD)and
which are linear independent (LI)?
(a) sin 2 cos , sin 2 cos , 2sin cos , 2 sin cos
(Ans: LI)
(b) 1 2, 2 3 , 3 4
APSC246-Assignment 10 (Due: 4:00PM Dec.3) 2012
2 pages and 4 Questions
Problem 1 (10 points) As we learned in Class, one of the LTI system properties is that if the
system input is , then assuming zero initial conditions, the system output is
, where is
APSC246-Assignment 4 (Due 4:00PM, Oct. 12) 2012
Problem 1 (5 points) Verify if the given functions are solutions of the given differential
equation.
2 9 sin2
, given functions: (i)
sin ; (ii)
3 sin ; (iii)
Problem 2 (5 points) Determine the o
APSC246-Assignment 1 (Due 4:00PM, Sept. 21) 2012
Problem 1: (10 points) For the signal x(t) illustrated below,
Sketch the signals.
(a) x(-t)
(b) x(t+6)
(c) x(3t)
(d) x(t/2)
Problem 2: (10 points) Consider the system whose input-output relationship is give
APSC246-Solutions to Assignment 8 2012
Total is 100/100
Problem 1 (5 points) cos sin cos , where ,
tan . Re-express each of the following expressions in the form of cos .
(a) 6 cos sin ;
(b) 3 cos 6 4 sin 6;
(c) 2 sin 3 2 cos 3
Solution:
(a)
(b)
(c)
Note
APSC246-Assignment 1 (Due 4:00PM, Sept. 28) 2012
Problem 1: (10 points) Simplify the following expressions:
(a) cos 3 (Ans: )
(b)
(Hint: Use LHopitals rule on
(c) 41 (Ans: 5)
) (Ans: )
(d) ! cos " 5 " 3" (Ans: 0)
Problem 2: (10 points) In class, we ha
APSC246-Assignment 8 (Due Nov. 19, 4:00PM) 2012
This assignment has 2 pages. Total is 100 points
Problem 1 (10 points) cos sin cos , where ,
tan . Re-express each of the following expressions in the form of cos .
(a) 6 cos sin ;
(b) 3 cos 6 4 sin 6;
(c)