What Values of C Cause Resonance in a Linear System with Given Solutions?

lukepeterpaul
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Hi,
Say if the complementary solution to a linear system is
A(coswt, coswt-wsinwt)+B(sinwt, wcoswt+sinwt)
and the forcing term is (coswt, coswt-Csinwt), where C is constant
How do I tell whether for what values of C is resonance going to occur?
Thanks!
 
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Resonance will occur for any value of C. It is the "w" that is important, not C.
 


Thanks, HallsofIvy. :)
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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