L4-5 - Vibrating string Classical wave equation amplitude...

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Vibrating string

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Classical wave equation amplitude
Classical wave equation Superposition of normal modes ω n = n π v/L

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How do we determine the solutions of the wave equation? Step 1 : fnd the solution oF the wave equation that are oF the special Form u(x,t) = X(x)T(t) For some Function X(x) that depends on x but not on t, and some Function T(t) that depends on t but not on x separation oF variables. IF we fnd a solution oF this Form, since the wave equation is a LINEAR equation, then linear combinations Σ i a i X i (x)T i (t) will be solutions For any choice oF the constant a i Step 2 : impose boundary conditions (conditions on variable x) Step 3 : impose initial conditions (conditions on variable t)—steps 2 and 3 will lead us to determine the constants a i
Solutions of the wave equation: separation of variables Step 1 : fnd the solution oF wave equation that are oF the special Form u(x,t) = X(x)T(t) For some Function X(x) that depends on x but not on t and some Function T(t) that depends on t but not on x

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This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

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L4-5 - Vibrating string Classical wave equation amplitude...

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