# How to get tau for every c and plot a c vs tau graph

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Atom on 16 Apr 2013
How to get tau for every c from the equation "tau=acos(((omega^2*(D1-A*B)-C*D1)/(B^2*omega^2+D1^2))/omega)" where A, B, C, D1, omega, x, y depends on c.
clc
clear
close all
r=3.3;
K=898;
alpha=0.045;
d=1.06;
h=0.0437;
theta=0.215;
for c=.1:.1:.9
x=d/(alpha*(theta - d*h)*(1 - c));
y=r*(K-x)*(1+alpha*h*x*(1-c))/(1 - c)*K*alpha;
A=r*d*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/(alpha*theta*K*(1-c))-d;
B=d;
C=-r*d^2*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/alpha*theta*K*(1-c);
D1=r*d^2*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/x*theta*K*(1-c)+r*d^2*(K-x)/alpha*K*theta*(1-c)*x;
omega=sqrt(((A^2-B^2-2*C)+sqrt((A^2-B^2-2*C)^2-4*(C^2-D1^2)))/2);
tau=acos(((omega^2*(D1-A*B)-C*D1)/(B^2*omega^2+D1^2))/omega);
plot(c,tau)
end

Iman Ansari on 16 Apr 2013
Hi
clc
clear
close all
r=3.3;
K=898;
alpha=0.045;
d=1.06;
h=0.0437;
theta=0.215;
i=1;
for c=.1:.1:.9
x=d/(alpha*(theta - d*h)*(1 - c));
y=r*(K-x)*(1+alpha*h*x*(1-c))/(1 - c)*K*alpha;
A=r*d*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/(alpha*theta*K*(1-c))-d;
B=d;
C=-r*d^2*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/alpha*theta*K*(1-c);
D1=r*d^2*(alpha*K*h*(1-c)-1-2*alpha*h*(1-c)*x)/x*theta*K*(1-c)+r*d^2*(K-x)/alpha*K*theta*(1-c)*x;
omega=sqrt(((A^2-B^2-2*C)+sqrt((A^2-B^2-2*C)^2-4*(C^2-D1^2)))/2);
tau(i)=acos(((omega^2*(D1-A*B)-C*D1)/(B^2*omega^2+D1^2))/omega);
i=i+1;
end
plot(.1:.1:.9,tau)
Atom on 16 Apr 2013
Thank you Mr Ansari. Your work helps me a lot. Thank you. Hope I will get help from you in future.