1. For the beams shown in Figure P16–11, determine the natural frequencies using first two and then.


1. For the beams shown in Figure P16–11, indicate the natural frequencies using pristine two and then three elements. Let E; r, and A be constant for the beams.

2. Rework Problem 16.11 using a computer program after a while E =3  107 psi, r = 0:00073 lb-s2/in4, A = 1 in2, L = 100 in., and I = 0:0833 in4.