Question

The motor weighs 20 lb and is supported on four springs where k = 25 lb/in for each spring. 3-lb weights are on the ends of two cantilever beams attached to the motor. EI = 2000 lb-in” for the cantilever beams and the length of each beam is l = 10 in. The vector-matrix form of the system model is: 4356 0 0 Ti [112 -6 -6 Yuse 0 , + -6 6 0 %386L, -60 Mä + Kx = 0 0 0 0 0 6 The system is initially at rest in its equilibrium position when the 3-lb weight on the left side is given an initial velocity of x,0) = 50 in/sec while x(0) = <3(0) = 0. Use modal decomposition to find the system's free response. 3 lb 3 lb EI EI ms 20 lb Motor k= 25 lb/in each Answer: <, (t) = +0.1392 sin (25.56t) -0.0745 sin(47.75t) in. x,(t)= +0.9067 sin (25.56t)+0.8998 sin (27.78t) +0.0382sin (47.75t) in. xy(t) = +0.9067sin (25.56t) - 0.8998 sin (27.78t)+0.0382 sin (47.75t) in.

Answer 1

please give some positive rating..i have less cf score..

Matlab Code: clear;clc; syms w; M = (20/386 0 0:0 3/386 0;0 0 3/386); K = (112 -6 -6;-6 6 0;-6 0 6); %natural frequencies e = det(M*w^2 - K); W = solve(e); W = vpa(W(W>0)); W = sort(W,'ascend'); %modes for i = 1:3 syms al a2; a3 = 1; p = W(i); A = (M*p^2 - K)*[al; a2; a 3]; V(i) = solve(A(1:2)); end ul = vpa([V(1).a1 V(1).a2 1]');%mode 1 u2 = vpa([V(2).al V(2).a2 1]');%mode 2 u3 = vpa([V(3).a1 V(3).a2 1]');%mode 3 U = [ul u2 u3]; %solving with initial conditions syms ABC; v = (0 50 O]': Q = (u1*W(1) u2*W(2) u3*W(3)]; E = Q*[A; B; C] - V; (a,b,c} = solve(E); Coeffs_Matrix = vpallu1*a u2*b u3*c]); Final Coefficient Matrix(same as answer): Coeffs_Matrix = [ 0.13924012929772576949448378265349, 0, -0.074539733225750313905408512604653) [ 0.90671565148760567380020153687333, 0.69976968843586816764459501561066, 0.03815574035492181961169753283443) [ 0.90671565148760567380020153687333, -0.89976968843586816764459501561066, 0.03815574035492181961169753283443]

Thank You So Much..