CHEM 4502 Lecture Notes - Lecture 4: String Vibration, Eigenfunction, Skipping Rope
Document Summary
If both sides equal to one another, can also set them equal to a constant. Chem4502 quantum page 1 trying to solve for u(x,t) --> find eqns for x(x) and t(t) that satisfy previous eqns and boundary conditions of vibrating wave problem. In this class, all diff eqs can be solved by intelligent guesses. Guess k = 0 --> integrate --> recall boundary conditions: u(0,t) = x(0)t(t) = 0 and u(l,t) = x(l)t(t) = 0. We can then work out that the only way to solve the above eqns is to have a1 and b1 = 0. -> this means string is flat at all times and doesn"t move. 0, need to find eqn that would satisfy our 2 eqns. General solution turns out to be when k is negative, solution is i = sqrt(-1) use euler"s identity to recast the answer as.
