MA232_Project_Fall08

MA232_Project_Fall08 - MA232 Numerical Project Fall 2008...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA232 Numerical Project Fall 2008 Due 9/19 1 Reduction of Order The numerical methods that we will look at this week are good for solving 1 st order DE’s. However, we wish to model 2 nd order DE’s because they are more interesting. This is O.K. because we can reduce 2 nd order DE’s into systems of 1 st order DE’s. An example: Hooke’s law is m d 2 x dt 2 =- kx , which is 2 nd order. If we define dx dt = V x , putting this into above, Hooke’s law is now m dV x dt =- kx . These boxed equations represent our new 1 st order system of DE’s. Note that before we only had one dependent variable: x . Now, in our system, we have two dependent variables: x and V . For practice, reduce the following 2 nd order DE’s into systems of 1 st order DE’s. Where applicable, please use the notation dθ dt = ω , dx dt = V x , and dy dt = V y . (a) Harmonic Oscillator (mass-spring-damper system): d 2 x dt 2 + c dx dt + kx =0 (reduce to two 1 st order DE’s) (b) Pendulum: d 2 θ dt 2 + g L sin...
View Full Document

This note was uploaded on 08/31/2009 for the course MA 232 taught by Professor Toland during the Spring '08 term at Clarkson University .

Page1 / 5

MA232_Project_Fall08 - MA232 Numerical Project Fall 2008...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online