# Homework Help: Steady state solution

1. Sep 14, 2007

### kasse

1. The problem statement, all variables and given/known data

What is the steady state solution to the equation

4y''+4y'+17y=202cos3t (*) ?

2. The attempt at a solution

The steady state solution is, if I've got it right, only the particular solution. It's got to be on the form

Kcos3x+Msin3x.

I calculate the derivatives, put into (*) and find it to be 122,19 cos 3t + 210 sin 3t.

It's normal to write steady state solutions on the form

Ccos(ωt-η).

How can I do that?

2. Sep 14, 2007

### genneth

If I tell you that K cos(A+B) = K cos A cos B - K sin A sin B = C cos A + D sin A,

could you find B and K if you were given C and D ?

3. Sep 14, 2007

### kasse

K=sqrt(C^2+D^2)

tan B =D/C

Found some formulas on the internet. Is it correct?

Last edited: Sep 14, 2007