Characterize the separated solutions to the PDE u_tt = u_xxxx in general. The fu
ID: 3802509 • Letter: C
Question
Characterize the separated solutions to the PDE u_tt = u_xxxx in general. The further restrict to the following sets of boundary conditions. This equation is used to model vibrations in an elastic beam, like a bridge, a flagpole, or a supporting beam in a house. (a) u_x (0, t) = u_x(pi, t) = 0 and u(0, t) = u(pi, t) = 0 (two supported ends) (b) u_xx (0, t) = u_xx(pi, t) = 0 and u(0, t) = u(pi, t) = 0. (two clamped ends) (c) u(0, t) = 0, u_x(0, t) = 0, u_xx(pi, t) = u_xxx(pi, t) = 0. (one clamped end, one free end)Explanation / Answer
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