(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the following underdamped oscillator governed by:

u''(t) + ¥u'(t) + w_{0}^{2}u(t)=Fcos(wt)

(a) Find the ge......

(b) The hom....

(c) What is the forcing frequency w for which the amplitude R in the previous part attains a maximum? Show that it is always less than the natural frequency w_{0}.

2. Relevant equations

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3. The attempt at a solution

So, I solved the problem in part (a) and put it in the form Rcos(wt-µ) in part (b). I've looked over my work several times; the answer is messy. You can try it for yourself if youreallyfeel like it. Otherwise, trust me when I say that the long term solution (getting rid of the homogenous equation since it involves crap in the form e-^{at}, where a is positive) is

[F(w_{0}2-w^{2})]/[(w_{0}^{2}-w^{2})^{2}+(wy)^{2}]*√[1+(wy)^{2}/(w_{0}^{2}-w^{2})^{2}]*cos(wt-tan^{-1}(wy/(w_{0}^{2}-w^{2})).

.....so how do I find the right w to maximize the amplitude? I have no idea. Please explain in detail. This assignment is due tomorrow morning.

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# Homework Help: Finding the forcing frequency to maximize the amplitude

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