# Thread: Method of Undetermined Coeffiicients Problem

1. ## Method of Undetermined Coeffiicients Problem

I have to find the steady state sinusoidal solution for the equation y''+2y'+10y=cos(wt), w>0. w is supposed to be omega by the way. How am I supposed to solve this for its steady state solution? I already had to solve for a equation where the omega was replaced by a 3 but I don't know what to do now that it is a omega.

Also if it is at all possible could you help me solve y''+2y'+10y=cost(3t) for it's steady state solution (i think I have it right but I just want to double check). I also need to find the amplitude (which I know how to get if the solution I have is correct) and the phase shift (which I don't know how to get) of the steady state solution.

If anyone could help with either problem it would be greatly appreciated.

2. Hi,

When solving steady-state harmonic problems like this, the beginning assumption is that your solution will also be steady-state harmonic, oscillating at the same frequency as the input, but with a phase shift. So, start by assuming:

$y=A cos(\omega t+\phi)$

You can then find the time derivatives of y and plug them into the original equation to solve for $A$ (magnitude of the solution) and $\phi$ (phase shift).