if + for loops vs while loop. Same good different results

Hello people,

So I am doing an online course. And I am stuck in one of the problems. I have to calculate the period of a pendulum.

This is my code:

function [ T ] = pendulum( L,a0 )
g = 9.8;
a = [];
omega = 0;
theta = a0;
dt = 10^-6;
for time = 0:dt:10
       a = g*sin(theta)/L;
       omega = omega + a*dt;
       theta = theta - omega*dt;
       if theta >= 0
           T = 4*time;
       else
           break
       end      
end

This is the correct answer:

function [ T ] = pendulum( L,a0 )
%PENDULUM Summary of this function goes here
%   L positive scalar
%   a0 positive scalar less than pi 

% alpha = angluar acceleration
% g = acceleration due to gravity
% omega = angular velocity

if L <=0
    fprintf('L must be a positive real number')
    T=0
    return
end
    

theta=a0;
g=9.8;
omega=0;
deltat=1e-6;

T=0;
while theta>0
    T=T+deltat;
    alpha=g*sin(theta)/L;
    omega=omega+alpha*deltat; 
    theta=theta-omega*deltat;
end
T=4*T
%formula=T/(2*pi*sqrt(L/g))
end

For L = 2 and a0 = pi/2

my code gives:

3.350336000000000

the correct code gives:

3.350344000012992

So the only difference between the two codes is that I used an if loop inside a for loop and the correct loop used only a while loop. Any ideas what could be the problem?

Thanks

Answer 1

[Stephen23]

Work backwards from the end, and look at where the time / T value last changes. They are not the same. The location of the the if and break is important, and/or the logical condition that you use.

Both of these give the same output (to within floating point tolerances):

for time = 0:dt:10
    if theta<0
        break
    end 
    a = g*sin(theta)/L;
    omega = omega + a*dt;
    theta = theta - omega*dt;     
end
T = 4*time

And

while theta>0
    T=T+dt;
    alpha=g*sin(theta)/L;
    omega=omega+alpha*dt; 
    theta=theta-omega*dt;
end
T = 4*T

[Stephen23]

Orestis Stylianou's "Answer" moved here:

Yes, you are right. Thanks for the help!

[Stephen23]

@Orestis Stylianou: I hope that it helped. Please remember to accept my answer!