# 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 $$z = z_{homog.} + z_{partic.}$$.