I

Since

\2J |(-1)- (/odd), the generalized equations of motion become

F0l(O(-l)~ ('odd). The corresponding general solutions are

= Ai sin(&)/f) + Bj cos(coit) + C, (/' odd). Consider the finite initial displacement

This last equality will be multiplied by sin( j it x/£ ) and integrated over the length of the string to yield

. / 4lrx\ . (jltx\ fl . (iirx\ . (j irx\ in I - I sin I :- \ dx — > R. I sin I - I sin I :- I , h [ sin (4;A) sin (/;A) dx ± Bj [ sin ^ , ) dx

These integrals can easily be evaluated by noting the orthogonality property of the sine functions. The result gives the following values for the constants B, :

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