*Please solve the above task B using MATLAB only.*

_

Please read carefully and find below the solution of a very similar question for part b.

*Task b Solution to a similar question* For you to use as a guide only!

% four_dof

function four_dof

t = 0:0.01:5 ; % time scale

c1 = 0 ;

c2 = 0 ;

c3 = 0 ;

c4 = 0 ;

k1 = 3200000 ;

k2 = 2600000 ;

k3 = 2000000 ;

k4 = 1500000 ;

m1 = 2500 ;

m2 = 3000 ;

m3 = 3000 ;

m4 = 1500 ;

init_x1 = 0.005 ;

init_v1 = 0 ;

init_x2 = 0.006 ;

init_v2 = 0 ;

init_x3 = 0.008 ;

init_v3 = 0 ;

init_x4 = 0.012 ;

init_v4 = 0 ;

init_y1 = init_x1 ;

init_y2 = init_v1 ;

init_y3 = init_x2 ;

init_y4 = init_v2 ;

init_y5 = init_x3 ;

init_y6 = init_v3 ;

init_y7 = init_x4 ;

init_y8 = init_v4 ;

initial = [init_y1 init_y2 init_y3 init_y4 ...

init_y5 init_y6 init_y7 init_y8];

[t,y]=ode45(@rhs,t,initial);

plot(t,y(:,1), t,y(:,3),t,y(:,5), t,y(:,7));

xlabel('t'); ylabel('x') ;

legend('x1 num','x2 num','x3 num', 'x4 num');

function dydt=rhs(t,y)

dydt_1 = y(2);

dydt_2 = -(c1+c2)*y(2)/m1 +c2*y(4)/m1-(k1+k2)*y(1)/m1+

k2*y(3)/m1 ...

+ f1(t)/m1 ;

dydt_3 = y(4);

dydt_4 = c2*y(2)/m2-(c2+c3)*y(4)/m2+k2*y(1)/m2-

(k2+k3)*y(3)/m2 ...

+k3*y(5)/m2+c3*y(6)/m2+f2(t)/m2 ;

dydt_5 = y(6);

dydt_6 = c3*y(4)/m3-(c3+c4)*y(6)/m3+k3*y(3)/m3-

(k3+k4)*y(5)/m3 ...

+k4*y(7)/m3+c4*y(8)/m3+f3(t)/m3 ;

dydt_7 = y(8);

dydt_8 = k4*y(5)/m4- k4*y(7)/m4 +c4*y(6)/m4- c4*y(8)/m4 +

f4(t)/m4 ;

dydt=[dydt_1;dydt_2;dydt_3;dydt_4;dydt_5;dydt_6;dydt_7;dydt_8]

;

end

function f_1 = f1(t)

f_1 = 0 ;

end

function f_2 = f2(t)

f_2 = 0 ;

end

function f_3 = f3(t)

f_3 = 0 ;

end

function f_4 = f4(t)

f_4 = 0 ;

end

end

The model and the parameters Figure 1 is a schematic of the four story shear building. Each floor is represented by its mass and the superstructure supporting each floor is idealized by a spring constant representing resistance to lateral motion and a damping coefficient providing frictional energy losses. External forces applied to each floor are ignored in this model, but the base (or the ground) may move during an earthquake. Hence, only four degrees of freedom are needed to describe total displacements of the structure, described as Figure 2 MA AN Base Figure A fou-story shear building excited by the base motion. k,kkk N4 0 Figure 2 A simplified four DOF model for a shear building