//determining critical value of K
s=%s
syms K
m=s^3+3408.3*s^2+1204000*s+1.5*10^7*K
cof_a_0 = coeffs(m,'s',0);
cof_a_1 = coeffs(m,'s',1);
cof_a_2 = coeffs(m,'s',2);
cof_a_3 = coeffs(m,'s',3);
    
r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3] 

n=length(r);
routh=[r([4,2]);r([3,1])];
routh=[routh;-det(routh)/routh(2,1),0];
t=routh(2:3,1:2); //extracting the square sub block of routh matrix
routh=[routh;-det(t)/t(2,1),0]
disp(routh,"rouths tabulation=")
routh(3,1)=0  //For marginaly stable system
sys=syslin('c',1.5*10^7/(s^3+3408.3*s^2+1204000*s))
k=kpure(sys)
disp(k,"K(marginal)=")
disp('=0',routh(2,1)*(s^2)+1.5*10^7*k,"auxillary equation")
p=poly([1.5*10^7*k,0,3408.3],'s','coeff') 
s=roots(p)
disp(s,"Frequency of oscillation(in rad/sec)=")