Please help this problem is due soon and I am VERY confused. THANK YOU!!!! A spr

Question

Please help this problem is due soon and I am VERY confused.

THANK YOU!!!!

A spring-mass system is shown below: In this figure, the masses of each block are designated as m1, m2, m3 and m4 and the spring constants of each spring are designated as k1, k2, k3 and k4. The force applied by a stretched spring is negative and is linearly proportional to its displacement (d) from equilibrium; ie, F spring = -kd. Knowing this, and using Newton's equations of motion (F = ma), we can write an equation relating the initial acceleration of each mass to its displacement: m1a1 = -k1d1 - k2(d2 - d1) m2a2 = -k2(d2 - d1) - k3(d3 - d2) m3a3 = -k3(d3 - d2) - k4(d4 - d3) m4a4 = -k4(d4 - d3) In this problem, we will assume that we have mounted an accelerometer in each block and so we can measure the initial acceleration imparted by the springs. We will solve for the initial displacements of the blocks, with the solution vector defined as d = [d1, d2, d3, d4]T Rearrange the right hand side of each individual equation so that it is in the form K1d1 + K2d2 - K3d3 + K4d4. The K coefficients should be in terms of the spring constants k1, k2, k3, and k4. From your code, display the results in the command window as a text string (you can write d_1, d_2, etc for the subscripts). Given the following masses, accelerations and spring constants, rewrite the system of equations into a single matrix equation of the form Kd = a where K is a square matrix of constant coefficients. To show that you have done this correctly, display your K and a matrices in the command window. What are the dimensions of K, d and a? Solve the matrix equation for d; display your results. (4 points) Create a variable (using the numerical values of m, a, k and d) called spring_mass_system which has the following format: Using element-by-element operations, compute the force which corresponds to the acceleration (ie, using Newton's law). Call this variable F_a and concatenate it with spring_mass_system as 6th column. Suppress your output. Compute the spring force acting on each mass (ie, solve your expressions from part 1 .a). Call this variable F_spring and concatenate it with spring_mass_system as a 7th column. Display spring_mass_system in the command window. What do you notice about F_a and F_spring?

Explanation / Answer

its a four degree system .

assuming that the solution is sinosodial .. a1= W^2*d1 ; a2= W^2*d2; a3= W^2*d3

equations can be further written in form of matrix to solve the using matlab ..

m1a1=-k1d1-k2(d2-d1);

m2a2=-k2(d2-d1)-k3(d3-d2);

m3a3=--k3(d3-d2)-k4(d4-d3);

m4a4=-k4(d4-d3);

can be written as

w^2*m1d1=-k1d1-k2(d2-d1);

w^2*m2d2=-k2(d2-d1)-k3(d3-d2);

w^2*m3d3=--k3(d3-d2)-k4(d4-d3);

w^2*m4d4=-k4(d4-d3);

Mass matrix = { [m1 0 0 0 ];[0 m2 0 0 ];[0 0 m3 0 ];[0 0 0 m4]}

Striffness matrix = {[-(k1-k2) -k2 0 0] ; [+k2 -(k2-k3) 0 0] ; [ 0 k3 -(k3-k4 0] ; [0 0 k4 -k4]}

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