The wave equation 2f t2 = c2 2f x2 we have been looking at models the movement of something like a guitar string, but it does not take into account any damping forces such as air resistance. The partial differential equation 2f t2 + f t = 2f x2 is an example of a damped wave equation, which models a guitar string which is subject to damping forces. (a) Find the general solution of the damped wave equation 2f t2 + f t = 2f x2 satisfying the boundary conditions f (t, 0) = f (t, ) = 0. (Please use the method we used to derive the solution of the wave equation; start by writing f (t, x) = k=1 bk(t) sin(kx) and finding differential equations satisfied by the coefficients bk(t).) Please give your answer in sigma notation, and also write out the first 3 nonzero terms in the series. (b) What can you say about lim t f (t, x)? Does this agree with your intuition, given what is being modeled