1 Newtons Second Law
The form of Newtons second law for three separate cases will be generated using quaternion operators acting on position quaternions. In classical mechanics, time and space are decoupled. One way that can be achieved algebraically is b
Interband and Intraband Optical Studies of CdSe Colloidal Nanocrystal Films
by
Fumiaki Toyama
B.A. Physics University of California, Berkeley, 2001 Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Master
ECE521
Linear Systems
Fall 2009
Homework 2: Due Septemper 24, in class
To the extent possible please type your homeworks. Note: You are free to use Matlab for calculations. However Matlab is not necessary for obtaining answers to any of the problems. Prob
ECE521
Linear Systems
Fall 2009
Homework 3: Due October 8, in class
To the extent possible please type your homeworks. Note: You are free to use Matlab for calculations. However Matlab is not necessary for obtaining answers to any of the problems. Problem
ECE521
Linear Systems
Fall 2009
Homework 4: Due Never
These are some practice problems that may help your preparation for the upcoming midterm exam. Problem 1 : Consider the continuous system: x(t) = 1 0 x(t) + 2 3 y(t) = [c1 c2 ]x(t) 1 2 u(t)
Under what
ECE521
Linear Systems
Fall 2009
Homework 5: Due November 5
Problem 1: Consider the system x = x(0) = -3 5 0 -3 x+ 0 1 1
u
0 1 y = [1 2] x
1. Find the transfer function G(s). 2. We know that y(t) = CetA x(0) +
0 y (0) (t) t
CeA(t- ) Bu( )d
Using Laplace tr
ECE521
Linear Systems
Fall 2009
Homework 5: Due November 19
Problem 1: Consider a continuous 0 0 A= 0 1
system defined by A and B, 1 0 1 0 0 0 0 0 1 0 , B= 0 0 0 0 1 0 1 1 -3 4
Find two different matrices K so the eigenvalues of A - BK are -1 i and -2 i
ECE521
Linear Systems
Fall 2009
Homework 1 Solutions
Problem 1: The example of a mechanical system given in lecture notes for Lecture 1 can be generalized to M q (t) + Lq(t) + Kq(t) = f (t), where q Rk is a vector of positions, f Rk is a vector of forces,
ECE521
Linear Systems
Fall 2007
Homework 2 Solutions
Problem 1 : Consider a 2 matrix A(t) which is continuous for all real t but is not invertible for any t. 1. As an example of such A(t), show that A(t) = a(t)b(t)T where a(t), b(t) R2 are continuous for
ECE521
Linear Systems
Fall 2009
Homework 3 Solutions
Problem 1: Consider a square matrix A for which det(A) = 0. Is it possible that det(etA ) = 0 for some finite t > 0? Justify your answer. We know that matrix exponential is a nonsingular matrix hence it
ECE521
Linear Systems
Fall 2009
Homework 4: Due Never
These are some practice problems that may help your preparation for the upcoming midterm exam. Problem 1 : Consider the continuous system: x(t) = 1 0 x(t) + 2 3 y(t) = [c1 c2 ]x(t) 1 2 u(t)
Under what
ECE521
Linear Systems
Fall 2009
Homework 5 Solutions
Problem 1: Consider the system x = x(0) = -3 5 0 -3 x+ 0 1 1
u
0 1 y = [1 2] x
1. Find the transfer function G(s). 2. We know that y(t) = CetA x(0) +
0 y (0) (t) t
CeA(t- ) Bu( )d
Using Laplace transfor
ECE521
Linear Systems
Fall 2009
Homework 6 Solutions
Problem 1: Consider a continuous 0 0 A= 0 1
system defined by A and B, 1 0 1 0 0 0 0 0 1 0 , B= 0 0 0 0 1 0 1 1 -3 4
Find two different matrices K so the eigenvalues of A - BK are -1 i and -2 i.
T T L
ECE521
Linear Systems
Fall 2009
Homework 1: Due September 10, in class
To the extend possible please type your homeworks. Problem 1: The example of a mechanical system given in lecture notes for Lecture 1 can be generalized to M q (t) + Lq(t) + Kq(t) = f