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
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
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
o
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
,
Solu
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 syste
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
APSC246 Solutions to Assignment #3 2012
Problem 1: (10 points) Sketch the following signals:
(a) u(t 5) u(t 7)
(b) u(t 5) +u(t 7)
(c) t2[u(t 1) u(t 2)]
(d) (t4)[u(t 2) u(t 4)]
where u(t) is the unit s
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 pr
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
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
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 co
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 zer
APSC246-Assignment 5 (Due 4:00PM, Oct. 23) 2012
Problem 1 (10 points) ( , ), find a general solution when , is homogeneous .
Show the steps of derivation.
(a)
(b)
,0
(Ans: 8 ln )
, 0, 0 (Ans:
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)
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
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