Suppose that the free end of the bar of Example 2 is
Chapter , Problem 12(choose chapter or problem)
Suppose that the free end of the bar of Example 2 is attached to a spring (rather than to a mass), as shown in Fig. 10.2.5. The endpoint condition then becomes ku.L; t / C AEux.L; t / D 0. (Why?) Assume that u.x; 0/ D f .x/ and that ut.x; 0/ D 0. Derive a solution of the form u.x; t / D X1 nD1 cn cos nat L sin nx L ; where fng 1 1 are the positive roots of the equation tan x D AEx=kL.
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