7.B7 Use separation of variables to solve this problem. solving: where: let w W(x) R(t) g R WIV + m R W 1 = 0 13 R a 2 WIV -R ----v2 EI and WIV a4 w a ml 4 -----;r ax The second equation above leads to the result that: Solving for W: 2 = w constant R + R w 2 R A sin wt+ B cos wt 2 WIV - ;. W a W = C sinh ~ x + D cosh ~ x + E sin~ x + F cos~ x a a a a remembering that: w WR By applying the appropriate boundary conditions, it is possible to determine the value of wand the magnitude of w. First, it is necessary to rewrite the above equation (7.Bl). let k = /2[ a W C[cos k x + cosh k x] + D[cos k x - cosh k x] + E[sinh x + sinh k x] + F[sinh x - sinh k x]
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