# Difference between revisions of "Problem 1d correction, hint"

For part (d) of problem 1 of Hw#2, every instance of ${\displaystyle t}$ should be replaced by ${\displaystyle \tau }$, so the wording should be changed to read: "Consider the case where ${\displaystyle \zeta =0}$ and ${\displaystyle v(\tau )=\sin \omega \tau ,\omega >1}$. Solve for ${\displaystyle z(\tau )}$, the normalized output of the oscillator, with initial conditions ${\displaystyle z_{1}(0)=z_{2}(0)=0}$."
If you've already solved it using ${\displaystyle t}$ instead of ${\displaystyle \tau }$ 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 ${\displaystyle z_{homog.}}$ from ${\displaystyle z=z_{homog.}+z_{partic.}}$.