For large t, every solution of d2 y dt2 + p dy dt + qy =
Chapter , Problem 6(choose chapter or problem)
For large t, every solution of d2 y dt2 + p dy dt + qy = cos t oscillates with angular frequency and amplitude A given by A(, p, q) = 1 (q 2)2 + p22 . That is, the amplitude A is a function of the parameters , p, and q. (a) Compute A/. (b) For fixed p and q, let M(p, q) denote the maximum value of A(, p, q) as a function of . Compute an expression for M(p, q). [Hint: This is a max-min problem from calculus.]
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