Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Please solve with MATLAB. Please wright code in a code-like format. Vibrations i

ID: 3797355 • Letter: P

Question

Please solve with MATLAB. Please wright code in a code-like format.

Vibrations in mechanical structures can be modeled using systems of springs and blocks. Consider the three mass system below. The length of each unstretched spring is L and the width of each block is W. The total length of the system is L_T which includes the stretched length of each spring, (i.e. The length of the first stretched spring is L + X_1 etc.) Determine the equilibrium position by solving the system of linear equations below for the x values. k_1 = 1 N/m, k_2 = 2 N/m, k_3 = 3 N/m, k_4 = 4 N/m, W = 0.1m, L = 0.5m, L_T = 4m x_1 + x_2 + x_3 + x_4 = L_T - 4L - 3W k_1x_1 = k_2x_2 k_2x_2 = k_3x_3 k_3x_3 = k_4x_4

Explanation / Answer

Solution :

%% Vibration in Mechanical structures

clc;

close all;

clear all;

%% Program strats here

%% Constants

k1=1;

k2=2;

k3=3;

k4=4;

W=0.1;

L=0.5;

LT=4;

%% Frame the matrix with the coefficients

A=[ 1 1 1 1

k1 -k2 0 0

0 k2 -k3 0

0 0 k3 -k4];

%% constant matrix

B=[LT-4*L-3*W;0;0;0];

%% Calculate X

x=inv(A)*B;

%% display result

disp('The solution of x1 x2 x4 x4 is :')

disp(x)

OUTPUT:

The solution of x1 x2 x4 x4 is :

0.8160

0.4080

0.2720

0.2040