Just your everyday math kid (emoboygenius) wrote in diffeq,
Just your everyday math kid
emoboygenius
diffeq

pde prob

Two things
same related question:

The Setup:
U_tt - (c^2)U_xx = -rU_t
resistance r > 0 and constant
periodic source U(0,t) = U(L,t) = Ae^(iwt)

Questions:
first says show that you can get resonance as r -> 0 if w = m(pi)c/L
second show that friction can prevent resonance from occuring

Our teacher never went over this in class, and this is the only time it's mentioned in the book so yeah I don't really know what they are talking about
any ideas?

oh and it gives the possible solution for the PDE as U(x,t) = Ae^(iwt) sin(bx)/sin(bL) where b^2 c^2 = w^2 - irw

x-posted
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