Hi, i do not know where to post this so i just figured i leave this where there are most people viewing. I need help doing question 4 only. Thanks!!

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- Nov 28th 2012, 12:41 AMjoshua111Laplace Transformation question
Hi, i do not know where to post this so i just figured i leave this where there are most people viewing. I need help doing question 4 only. Thanks!!

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Attachment 25966 - Nov 28th 2012, 02:43 AMBobPRe: Laplace Transformation question
The steady state part can be expressed in the form

$\displaystyle v_{steady}=A\sin (\omega t + \alpha) = A\sin \omega t \cos \alpha + A \cos \omega t \sin \alpha,$

where $\displaystyle A $ is the amplitude.

Equate coefficients of $\displaystyle \sin \omega t$ and $\displaystyle \cos \omega t$ with the corresponding expressions in your formula for $\displaystyle v_{steady},$ and eliminate the $\displaystyle \cos \alpha \text{ and } \ sin \alpha$ by squaring and adding. - Nov 28th 2012, 02:50 AMjoshua111Re: Laplace Transformation question
- Nov 28th 2012, 05:30 AMBobPRe: Laplace Transformation question
If $\displaystyle A\sin \theta = p \text{ and } A\cos \theta = q,$

then ,squaring and adding,

$\displaystyle A^{2}(\sin ^{2}\theta + \cos ^{2}\theta) = p^{2} + q^{2},$

so

$\displaystyle A = \sqrt {p^{2} + q^{2}.$

And sorry, but I know absolutely nothing about the filters mentioned in the question. - Nov 28th 2012, 08:04 AMjoshua111Re: Laplace Transformation question
- Nov 28th 2012, 02:17 PMBobPRe: Laplace Transformation question
I didn't derive anything in post 2, I simply stated what should (at your stage) be a well-known trig identity, and what allows the the expression for $\displaystyle v_{steady}$ given in the question to be written in an alternative form.

Another trig identity, with which you should be familiar, is used later. $\displaystyle \cos^{2}\theta+\sin^{2}\theta=1.$