Problem 1d correction, hint
From MurrayWiki
For part (d) of problem 1 of Hw#2, every instance of t should be replaced by τ, so the wording should be changed to read: "Consider the case where ζ = 0 and v(τ) = sinωτ,ω > 1. Solve for z(τ), the normalized output of the oscillator, with initial conditions z1(0) = z2(0) = 0."
If you've already solved it using t instead of τ you will get equal credit (it is just a little bit more complex).
To solve this problem, you can use the "method of undetermined coefficients" (see, for example, http://www.efunda.com/math/ode/linearode_undeterminedcoeff.cfm) to solve for the steady-state frequency response solution. Then you can add to it a homogeneous solution that cancels the initial condition from the steady state so that the given initial conditions are satisfied. i.e., find zhomog. from z = zhomog. + zpartic..
--Sawyer Fuller 00:32, 15 October 2007 (PDT)
[Category: CDS 101/110 FAQ - Homework 2]
