# HW4 - term Hint See Chapter 5 of our text book or the class...

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

Math 401 (Sec. 502) Spring, 2009 Homework 4 (due February 19) Q1. Consider the following IVP (called damped linear oscillator) y ′′ + 2 ǫy + y = 0; y (0) = 0 , y (0) = 1 . (a) Compute the exact solution. (b) Use two-scale perturbation theory to Fnd a leading-order approxima- tion. (c) Then compute the second term of the solution. Do you get any secular term in this second term? If so, then, explain the signiFcance of that secular
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: term. [ Hint: See Chapter 5 of our text book or the class notes.] Q2. Use two-scale perturbation theory to Fnd a leading-order approximation to the non-linear ODE: y ′′ + y-ǫ [ y ′-1 3 ( y ′ ) 3 ] = 0; y (0) = 0 , y ′ (0) = 1 . [ Hint: You are given the solution to 2 dx dθ = x-1 4 x 3 , x (0) = 1 is x ( θ ) = 2 √ 1+3 e-θ ]...
View Full Document

## This note was uploaded on 04/27/2009 for the course MATH 401 taught by Professor Sarkar during the Spring '09 term at Texas A&M.

Ask a homework question - tutors are online