A uniform bar is clamped at x 0 and is initially at rest. If a constant force F0 is applied to the free end at x L, the longitudinal displacement u(x, t) of a cross section of the bar is determined from a2 02 u 0x 2 02 u 0t 2 , 0 , x , L, t . 0 u(0, t) 0, E 0u 0x 2 xL F0, E a constant, t . 0 u(x, 0) 0, 0u 0t 2 t0 0, 0 , x , L. Solve for u(x, t). [Hint: Expand 1/(1 e2sL/a ) in a geometric series.]

FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS I: Introduction and Analytic Methods David Levermore Department of Mathematics University of Maryland 22 January 2012 Because the presentation of this material in lecture will diﬀer...