If the bar in Example 2 has no mass attached to the end x
Chapter , Problem 8(choose chapter or problem)
If the bar in Example 2 has no mass attached to the end x D L, then Eq. (17c) is replaced with the free end condition ux.L; t / D 0. Separate variables in the resulting boundary value problem to derive the series solution u.x; t / D X1 nD1 cn cos .2n 1/at 2L sin .2n 1/x 2L ; where cn D 2 L Z L 0 bx sin .2n 1/x 2L dx D 8bL.1/nC1 .2n 1/22 : In particular, the bars natural frequencies of longitudinal vibration are given by Eq. (28). 9. (a)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer