My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 2nd, 2010, 01:00 PM   #1
Newbie
 
Joined: Feb 2010

Posts: 2
Thanks: 0

Diff EQ 2nd Order ODE

I just started graduate school in engineering. The class that I am taking is structural dynamics. It's been a number of years since I took diff eq, so I have forgotten quite a bit, though I have been reading my books. I can't seem to find anything that will help me with the homework that my professor has assigned. I hope that there is someone who can help explain things to me. The problem is below.

a) find the solution for:
m*y''+c*y'+ky=0
i) assume that c=0, y(0)=0, dy/dx (0)=0
Comments: I understand what all this means. The diff eq describes dampened vibrations, with c=0, the equation describes simple harmonic motion. I know what the solution should look like (sin(sqrt(k/m)t))
ii) Assume c=0.5, k=0.5, m=0.5, y(0)=1, dy/dx (0)=0
iii) Assume c=2, k=0.5, m=0.5, y(0)=1, dy/dx =(0)=0
b) find the solution for:
m*y''+c*y'+k*y= sin(x)
i)Assume c=0.5, k=0.5, m=0.5, y(0)=0, dy/dx (0)=0

Like I said, I understand what all of this means. I remember the concepts but I just don't remember the math to make it happen.
I followed one of the examples in my diff eq book and it describes making an auxiliary equation, however, when the coefficients are variables, how am I to solve the resulting quadratic?
foy1der is offline  
 
February 2nd, 2010, 01:10 PM   #2
Newbie
 
Joined: Feb 2010

Posts: 2
Thanks: 0

Re: Diff EQ 2nd Order ODE

Just noticed I'm in the wrong forum. If one of the mods wants to move this to one of the college math sections, maybe that will help things.
foy1der is offline  
February 2nd, 2010, 07:27 PM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 20,755
Thanks: 2137

Quote:
Originally Posted by foy1der
I followed one of the examples in my diff eq book and it describes making an auxiliary equation, however, when the coefficients are variables, how am I to solve the resulting quadratic?
Assume the coefficients are constants and use the quadratic formula. You may need to consider whether the coefficients are positive, zero or negative.
skipjack is online now  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
2nd, diff, ode, order



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Is this allowed?? (First order ODE) Exact Diff Eqn hanilk2006 Calculus 1 October 2nd, 2013 05:01 PM
Runge-Kutta 4 for a second order diff-eq. Please help arogyth Applied Math 0 July 22nd, 2013 01:22 PM
Runge-Kutta 4 for a second order diff-eq. Please help arogyth Calculus 1 July 22nd, 2013 01:19 PM
1st order diff equations mathkid Calculus 5 September 10th, 2012 03:10 PM
Solving 2nd order nonlinear diff eq lu5t Applied Math 0 April 30th, 2012 09:59 AM





Copyright © 2019 My Math Forum. All rights reserved.