# ODE45: IF/loop function

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Komal Rajana on 9 Jan 2020
Answered: Jyothis Gireesh on 12 Feb 2020
Hello,
I would like to know if its correct to write my differential equations as follow in the 'if' command in the function file. If not, please advice. I am trying to model a simple damper.
Thanks.
function [dy] = SDOF2(t, u);
dy = zeros(2,1);
m=1000; %Mass (lb.sec^2/in.)
k =100000; %Stiffness (lb/in.)
omega = sqrt(k/m); %Natural Frequency
c=2000;%Damping coefficient (lb.sec/in.)
g =386;%Acceleration of gravity (in./sec^2)
c_cr=2*m*omega; %Critical damping coefficient
xi = c/c_cr;%Damping ratio
%%Define the forcing function
% if t<=0.5
% F = sin(4*pi*t);
% else
% F =0;
F = 0;
% b=1*m*(((-omega*omega*u(1)-2*xi*omega*u(2)+F))/u(2)>0);
% end %%%%-ESTIMATION-%%%%
if ((((-omega*omega*u(1))-(2*xi*omega*u(2))+F/m)/u(2))>0)
dy(1) = u(2);
dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m-0.5*m*((-omega*omega*u(1))-(2*xi*omega*u(2))+F/m);
else
dy(1) = u(2);
dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m;
end
% dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m;
end
Aquatris on 10 Jan 2020
There are a lot of examples online, here is on of them.

Jyothis Gireesh on 12 Feb 2020
It is my understanding that the differential equation is a function of “u(1)” and “u(2)”. So it is safe to assume that “u(1)” and “u(2)” are symbolic variables (or can be defined as symbolic). In this case, it may be better to use the “piecewise” function which allows conditionally defined expressions or functions.
Please refer to the following documentation link to get information on “piecewise” function