Problem 1d correction, hint

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For part (d) of problem 1 of Hw#2, every instance of t should be replaced by \tau , so the wording should be changed to read: "Consider the case where \zeta =0 and v(\tau )=\sin \omega \tau ,\omega >1. Solve for z(\tau ), the normalized output of the oscillator, with initial conditions z_{1}(0)=z_{2}(0)=0."

If you've already solved it using t instead of \tau 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 z_{{homog.}} from z=z_{{homog.}}+z_{{partic.}}.

--Sawyer Fuller 00:32, 15 October 2007 (PDT)

[Category: CDS 101/110 FAQ - Homework 2]