wnt = 0:12/100:12; y0 = 5; %%%%% part A %%%% zeta1 = .05; zeta2 = .1; theta1 = a
ID: 2268181 • Letter: W
Question
wnt = 0:12/100:12;
y0 = 5;
%%%%% part A %%%%
zeta1 = .05;
zeta2 = .1;
theta1 = acos(zeta1);
theta2 = acos(zeta2);
beta1 = sqrt(1-zeta1^2);
beta2 = sqrt(1-zeta2^2);
ya1 = size(wnt); ya2 = size(wnt);
for i = 1:101
ya1(i) = (y0/beta1)*exp(-zeta1*wnt(i))*sin(beta1*wnt(i)+theta1);
ya2(i) = (y0/beta2)*exp(-zeta2*wnt(i))*sin(beta2*wnt(i)+theta2);
end
wnTb = 2*pi/beta1;
plot(wnt,ya1,'bo',wnt,ya2,'r')
title(' A');
legend('zeta = .05','zeta = 0.1')
xlabel('wn*t'),ylabel('Response');
%%%%%PART B%%%%%%
zetab = [.2,.3,.4,.5,.7,.9];
thetab = acos(zetab);
betab = sqrt(1-zetab.^2);
K = 4;
yb = zeros(101,6);
u = 1 ;
for i = 1:101
for j = 1:6
yb(i,j) = (K*u)-(K/betab(j))*exp(-zetab(j)*wnt(i))*sin(betab(j)*wnt(i)+thetab(j));
end
end
figure
plot(wnt,yb)
title(' B')
legend('zeta = 0.2','zeta = 0.3','zeta = 0.4','zeta = 0.5','zeta = 0.7','zeta = 0.9')
xlabel('wn*t'),ylabel('Response');
%%%%% PART C %%%%%%
zeta3 = 0.99;
theta3 = acos(zeta3);
beta3 = sqrt(1-zeta3^2);
yc1 = size(wnt); yc2 = size(wnt);
for i = 1:101
yc1(i) = y0*exp(-wnt(i))*(1+wnt(i));
yc2(i) = (y0/beta3)*exp(-zeta3*wnt(i))*sin(beta3*wnt(i)+theta3);
end
figure
plot(wnt,yc1,'bo',wnt,yc2,'r+')
title(' C');
legend('zeta = 1(critically damped)','zeta = 0.99')
xlabel('wn*t'),ylabel('Response');
OBJECTIVE; MANIPULATE THIS MATLAB CODE TO LOOK NOTHING LIKE THE ORGINAL BUT STILL GIVES SAME OUTPUT.
46 × Answer 1 of 1 Knon in E>?"c.ned ne 1 Kreu na R.se.H'rnetH.) -3Explanation / Answer
fs = 100/12;
wn_t = 0:1/fs:12;
y_0 = 5;
%% %%%%%part A %%%%
z_1 = .05;
z_2 = .1;
th_1 = acos(z_1);
th_2 = acos(z_2);
bt_1 = sqrt(1-z_1^2);
bt_2 = sqrt(1-z_2^2);
y_a1 = size(wn_t); y_a2 = size(wn_t);
for i = 1:101
y_a1(i) = (y_0/bt_1)*exp(-z_1*wn_t(i))*sin(bt_1*wn_t(i)+th_1);
y_a2(i) = (y_0/bt_2)*exp(-z_2*wn_t(i))*sin(bt_2*wn_t(i)+th_2);
end
wn_t_b = 2*pi/bt_1;
plot(wn_t,y_a1,'ro',wn_t,y_a2,'b')
title('Part A');legend('Zeta = .05','Zeta = 0.1'); xlabel('Wn*t'),ylabel('Response');
%% %%%%%PART B%%%%%%
z_b = [.2,.3,.4,.5,.7,.9];
th_b = acos(z_b);
bt_b = sqrt(1-z_b.^2);
K = 4;
y_b = zeros(101,6);
l = 1 ;
for i = 1:101
for j = 1:6
y_b(i,j) = (K*l)-(K/bt_b(j))*exp(-z_b(j)*wn_t(i))*sin(bt_b(j)*wn_t(i)+th_b(j));
end
end
figure(2)
plot(wn_t,y_b); title('Part B')
legend('Zeta = 0.2','Zeta = 0.3','Zeta = 0.4','Zeta = 0.5','Zeta = 0.7','Zeta = 0.9')
xlabel('Wn*t'),ylabel('Response');
%% %%%%% PART C %%%%%%
z_3 = 0.99;
th_3 = acos(z_3);
bt_3 = sqrt(1-z_3^2);
y_c1 = size(wn_t); y_c2 = size(wn_t);
for i = 1:101
y_c1(i) = y_0*exp(-wn_t(i))*(1+wn_t(i));
y_c2(i) = (y_0/bt_3)*exp(-z_3*wn_t(i))*sin(bt_3*wn_t(i)+th_3);
end
figure(3)
plot(wn_t,y_c1,'ro',wn_t,y_c2,'b+')
title('Part C');
legend('Zeta = 1(critically damped)','Zeta = 0.99')
xlabel('Wn*t'),ylabel('Response');
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