ECE
hw11

# hw11 - ECE320 Homework 11 Cornell University Spring 2006...

• Homework Help
• 501844684_ch
• 1

This preview shows page 1. Sign up to view the full content.

ECE320 Homework 11 Spring 2006 Cornell University T.L.Fine We have our third prelim on Thursday, 27 April. Please hand in this assignment at the close of lecture on Tuesday, 25 April. Use only your assigned three-digit code and not your name. I will post solutions to this homework shortly after 1pm on Tuesday the 25th. Throughout, give reasons for your answers. 1. Classify the following ode s as to whether they are autonomous and what their orders and degrees are: ( a ) ¨ x + ω 2 x = 0 , harmonic oscillator; ( b ) ¨ x - tx = 0 , Airy ode; ( c ) t 2 ¨ x + t ˙ x + ( λ 2 t 2 - n 2 ) x = 0 , Bessel’s equation; ( d ) ˙ x - tx 2 = e - t ; ( e ) tan(¨ x ) - x = 0; ( f ) ¨ x ˙ xx = sin( t ); ( g ) ( ˙ x ) 2 - x = 0; ( h ) ¨ x = - x 2 + sin( ω ˙ x ) . 2. Represent each of the ode s of Problem 1 in the standard form ˙ y = F ( y ), if possible. 3. For each of the representations in Problem 2, determine the equilibrium
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: points (states), if any. 4. Consider the ode of Problem 1(h) with initial condition s (0) = ( x (0) , ˙ x (0)) = (-1 , 0) and ω = 2. (a) Numerically integrate this equation over the time domain D = [0 , 1] using a ﬁrst-order Taylor’s series and time interval of .01 between steps. Submit a plot of x ( t ). (b) Repeat this task but use pplane7.m to perform the numerical integration process and submit a plot of x ( t ). (c) How similar are the results of (a) and (b)? 5. Repeat Problem 4 for ω = 20. How well do the results of your numerical integration compare with that of pplane7.m in this case? 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern