# Frequency vs Amplitude plot using ODE45

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ismail darwish on 25 Jul 2020
Answered: Priyanshu Mishra on 28 Jul 2020
I need to plot the Frequency vs Amplitude for this function.
function dy=newMFF(t,x)
global a b c d g omg
dy=zeros(2,1);
dy(1)=x(2);
dy(2)=- a*x(1)- b*x(2)* x(1)^2 - c*x(1)^3 -d*x(2)+g*cos(omg*t);
end
F = 1;
E=1.1e12;
row=1.3e3;
G=280e9;
L=50e-9;
h=0.3e-9;
w= 10*h;
gap= 4*h;
I=(1/12)*w*(h^3);
Ar=w*L;
v= 0.5;
mu=200e-6;
Po = 1e5;
Pa = 1e8;
lambda=64e-9;
lam = (lambda*Po)/(Pa*gap);
cpp = (mu*(L^2)*(w^3))/((gap^3)*sqrt(E*I*Ar*row))
Pr=10;
ssf = h^2;
eta = 3e7; %this value is highly significant
%Dimensionless quantities
zeta = (Ar*G*ssf)/(E*I);
alpha = 6*((gap/h)^2);
P= (Pr*L^2)/(E*I);
vel= (v*L)*sqrt((row*Ar)/(E*I));
beta = (eta*(L^4))/(E*I*gap^2);
cp = cpp / (1+6*lam);
g = (F*gap*L^-2)*(sqrt((E*I)/(row*Ar)));
%Coefficients
a = ((pi^4)*(zeta+1))-((pi^2)*((vel^2)-P));
b = (3/4)*beta;
c = 0.5*(pi^4)*alpha;
d = (cp*(L^2))/(sqrt(row*E*I*Ar));
wo=sqrt(a);
b = b*w^2/wo ;c=c*w^2/wo ;d=d/wo ;a=1;
eps=d;

Priyanshu Mishra on 28 Jul 2020
Hi Ismail
You may refer to following documentation for solving differential equation using ode45 and plotting your solutions: