Question

Vibration

solve 1.2 by using numbers (values) from 1.1

1.1 Determine the natural period for the system in Fig. P1.1. Assume that the beam and springs supporting the weight Ware massless. Fig. P1.1 1.2 The following numerical values are given in Problem 1.1: L = 100 in, EI - 10% (b.in), W=3000 lb, and k = 2000 lb/in. If the weight W has an ini- tial displacement of yo = 1.0 in and an initial velocity Vo = 20 in/sec, deter- mine the displacement and the velocity 1 sec later. Tada . . . . . . . . . . .. . . . . .

Answer 1

Calculate the equivalent stiffness due deflection of cantilever beam. _W 3E1 W_W 3E1 TE 3(10) (100) = 300 lb/in Calculate the natural frequency of the oscillating mass. (k+k+k') @nViVM |(2k+k) VM (2(2000)+(300)) 3000 32.2x12 (4300) 3000 (32.2x12 = 23.534 rad/sec Calculate the displacement after 1 sec.

y= y, sin ot =(1.0) sin (23.534) = sin 23.534t = sin ( 23.534x1) = -0.9996 in Calculate the velocity after 1 sec. vedyd, dt de (y sin ot) = y.@cosot = V, cos Ot =(20) cos( 23.534) = 20 cos (23.534x1) =-0.5588in/sec