MATLAB: Solving the pendulum differential equation with a for loop

differential equationsfor loophelpnewnewbieodestudent

Hi I'm trying to write down a code that solves the equation of the pendulum in the hyp of little swings.
The task is to write it with a for loop without using the ODEs functions.
the code i wrote obviusly doesn't work.
Does someone could help me?
equation of pendulum:
l*diff(c,t,2)+g*c==0
code I wrote:
l=50; %rope length
g=9.81; %g constant
t=0; %time
syms c;
Dc= diff(c,t);
cond= [c(0)==0, Dc(0)==0.1]; %initial conditions
T=7.5*pi*sqrt(l/g);
n=linspace(0, T, 1000);
for i=1:n %I need the c value at every 't' from 0 to T with 1000 points
 t= i;
 ode = l*diff(c,t,2)+g*c==0;
 sol=dsolve(ode,cond);
  %sol=dsolve(ode);
  
end

Best Answer

Hope this helps. The solution for the differential equation is obtained as cSol(t). The required solution is obtained as a row vector 'sol'
l=50; %rope length
g=9.81; %g constant
syms c(t);
Dc= diff(c,t);
ode = l*diff(Dc)+g*c==0;
cond=c(0)==0;
cond1=Dc(0)==0.1;
cSol(t)=dsolve(ode,[cond cond1]);
T=7.5*pi*sqrt(l/g);
n=linspace(0, T, 1000);
for i=1:length(n)
    sol(i)=double(cSol(n(i)));
end
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