# Problem 1d correction, hint

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]