BlogFor BusinessTalk to a counsellor
CoursesIIT ProgramsPlacementsLog in
BlogFor Business
Talk to a counsellor
Challenge

Week 3 - Solving second order ODEs

RRamachandran S16 Jul 2022
clear all
close all
clc
b=0.5;
g=9.81;
l=1;
m=0.1;
%inital condition
theta_0 =[0;5];
%time points
t_span = linspace(0,10,500);
% solve ODE
[t,results] = ode45(@(t,theta)ode_func(t,theta,b,g,l,m),t_span,theta_0);
plot(t,results(:,1))
hold on
plot(t,results(:,2))
ylabel('plot')
xlabel('time')
ode function program
function [dtheta_dt] =ode_func(t,theta,b,g,l,m)
theta1 = theta(1)
theta2 = theta(2)
dtheta1_dt = theta2;
dtheta2_dt = -(b/m)*theta2 - (g/l)*sin(theta1);
dtheta_dt = [dtheta1_dt; dtheta2_dt];
end
outputs


theta1 =

0


theta2 =

5


theta1 =

4.0190e-05


theta2 =

4.9998


theta1 =

6.0283e-05


theta2 =

4.9997


theta1 =

1.6075e-04


theta2 =

4.9992


theta1 =

1.7861e-04


theta2 =

4.9991


theta1 =

2.0093e-04


theta2 =

4.9990


theta1 =

2.0093e-04


theta2 =

4.9990


theta1 =

4.0184e-04


theta2 =

4.9980


theta1 =

5.0225e-04


theta2 =

4.9975


theta1 =

0.0010


theta2 =

4.9950


theta1 =

0.0011


theta2 =

4.9945


theta1 =

0.0012


theta2 =

4.9940


theta1 =

0.0012


theta2 =

4.9940


theta1 =

0.0022


theta2 =

4.9890


theta1 =

0.0027


theta2 =

4.9864


theta1 =

0.0052


theta2 =

4.9739


theta1 =

0.0057


theta2 =

4.9717


theta1 =

0.0062


theta2 =

4.9689


theta1 =

0.0062


theta2 =

4.9689


theta1 =

0.0112


theta2 =

4.9439


theta1 =

0.0137


theta2 =

4.9315


theta1 =

0.0260


theta2 =

4.8694


theta1 =

0.0282


theta2 =

4.8584


theta1 =

0.0309


theta2 =

4.8447


theta1 =

0.0309


theta2 =

4.8447


theta1 =

0.0552


theta2 =

4.7215


theta1 =

0.0667


theta2 =

4.6621


theta1 =

0.1235


theta2 =

4.3667


theta1 =

0.1333


theta2 =

4.3151


theta1 =

0.1453


theta2 =

4.2516


theta1 =

0.1450


theta2 =

4.2520


theta1 =

0.2518


theta2 =

3.6824


theta1 =

0.2891


theta2 =

3.4491


theta1 =

0.4808


theta2 =

2.2964


theta1 =

0.5301


theta2 =

2.0758


theta1 =

0.5568


theta2 =

1.8717


theta1 =

0.5228


theta2 =

1.9337


theta1 =

0.6436


theta2 =

1.0237


theta1 =

0.6400


theta2 =

0.8190


theta1 =

0.8292


theta2 =

-0.7364


theta1 =

1.1781


theta2 =

-1.8576


theta1 =

1.1753


theta2 =

-2.0565


theta1 =

0.6460


theta2 =

-0.5724


theta1 =

0.6017


theta2 =

1.3396


theta1 =

0.6138


theta2 =

1.1489


theta1 =

0.7215


theta2 =

0.0939


theta1 =

0.8150


theta2 =

-0.2814


theta1 =

0.8140


theta2 =

-0.4169


theta1 =

0.6838


theta2 =

-0.0614


theta1 =

0.6813


theta2 =

-0.3016


theta1 =

0.6690


theta2 =

-0.3658


theta1 =

0.6360


theta2 =

-0.7659


theta1 =

0.6729


theta2 =

-0.9706


theta1 =

0.6562


theta2 =

-1.0073


theta1 =

0.5844


theta2 =

-0.7683


theta1 =

0.5484


theta2 =

-0.8418


theta1 =

0.5266


theta2 =

-0.8435


theta1 =

0.4422


theta2 =

-0.9296


theta1 =

0.4621


theta2 =

-1.0653


theta1 =

0.4413


theta2 =

-1.0520


theta1 =

0.3859


theta2 =

-0.8473


theta1 =

0.3412


theta2 =

-0.8186


theta1 =

0.3206


theta2 =

-0.7885


theta1 =

0.2342


theta2 =

-0.7068


theta1 =

0.2412


theta2 =

-0.7929


theta1 =

0.2257


theta2 =

-0.7629


theta1 =

0.1921


theta2 =

-0.5998


theta1 =

0.1605


theta2 =

-0.5404


theta1 =

0.1482


theta2 =

-0.5102


theta1 =

0.0911


theta2 =

-0.3925


theta1 =

0.0861


theta2 =

-0.4181


theta1 =

0.0780


theta2 =

-0.3947


theta1 =

0.0718


theta2 =

-0.3226


theta1 =

0.0554


theta2 =

-0.2766


theta1 =

0.0499


theta2 =

-0.2575


theta1 =

0.0215


theta2 =

-0.1719


theta1 =

0.0147


theta2 =

-0.1686


theta1 =

0.0113


theta2 =

-0.1551


theta1 =

0.0153


theta2 =

-0.1388


theta1 =

0.0086


theta2 =

-0.1124


theta1 =

0.0066


theta2 =

-0.1028


theta1 =

-0.0045


theta2 =

-0.0553


theta1 =

-0.0091


theta2 =

-0.0466


theta1 =

-0.0100


theta2 =

-0.0402


theta1 =

-0.0054


theta2 =

-0.0426


theta1 =

-0.0073


theta2 =

-0.0306


theta1 =

-0.0077


theta2 =

-0.0267


theta1 =

-0.0104


theta2 =

-0.0060


theta1 =

-0.0124


theta2 =

9.2533e-05


theta1 =

-0.0124


theta2 =

0.0025


theta1 =

-0.0098


theta2 =

-0.0023


theta1 =

-0.0099


theta2 =

0.0027


theta1 =

-0.0097


theta2 =

0.0040


theta1 =

-0.0094


theta2 =

0.0120


theta1 =

-0.0105


theta2 =

0.0163


theta1 =

-0.0102


theta2 =

0.0168


theta1 =

-0.0083


theta2 =

0.0117


theta1 =

-0.0077


theta2 =

0.0128


theta1 =

-0.0074


theta2 =

0.0127


theta1 =

-0.0061


theta2 =

0.0139


theta1 =

-0.0065


theta2 =

0.0161


theta1 =

-0.0062


theta2 =

0.0158


theta1 =

-0.0052


theta2 =

0.0124


theta1 =

-0.0046


theta2 =

0.0118


theta1 =

-0.0043


theta2 =

0.0113


theta1 =

-0.0030


theta2 =

0.0099


theta1 =

-0.0032


theta2 =

0.0112


theta1 =

-0.0029


theta2 =

0.0108


theta1 =

-0.0025


theta2 =

0.0083


theta1 =

-0.0020


theta2 =

0.0074


theta1 =

-0.0019


theta2 =

0.0070


theta1 =

-0.0011


theta2 =

0.0052


theta1 =

-0.0010


theta2 =

0.0055


theta1 =

-9.1636e-04


theta2 =

0.0051


theta1 =

-8.7258e-04


theta2 =

0.0043


theta1 =

-6.5761e-04


theta2 =

0.0037


theta1 =

-5.8648e-04


theta2 =

0.0034


theta1 =

-2.1494e-04


theta2 =

0.0022


theta1 =

-1.1612e-04


theta2 =

0.0021


theta1 =

-7.3738e-05


theta2 =

0.0019


theta1 =

-1.4259e-04


theta2 =

0.0018


theta1 =

-5.4799e-05


theta2 =

0.0014


theta1 =

-3.1483e-05


theta2 =

0.0013


theta1 =

1.1057e-04


theta2 =

6.2229e-04


theta1 =

1.7696e-04


theta2 =

4.8492e-04


theta1 =

1.8736e-04


theta2 =

4.0234e-04


theta1 =

1.1366e-04


theta2 =

4.6341e-04


theta1 =

1.3634e-04


theta2 =

2.9543e-04


theta1 =

1.3844e-04


theta2 =

2.4543e-04


theta1 =

1.6819e-04


theta2 =

-3.5719e-05


theta1 =

2.0269e-04


theta2 =

-1.3899e-04


theta1 =

2.0052e-04


theta2 =

-1.6563e-04


theta1 =

1.5095e-04


theta2 =

-6.6244e-05


theta1 =

1.4739e-04


theta2 =

-1.2796e-04


theta1 =

1.4189e-04


theta2 =

-1.3808e-04


theta1 =

1.3001e-04


theta2 =

-2.2969e-04


theta1 =

1.5061e-04


theta2 =

-3.0808e-04


theta1 =

1.4520e-04


theta2 =

-3.0809e-04


theta1 =

1.0836e-04


theta2 =

-2.0253e-04


theta1 =

9.2861e-05


theta2 =

-2.0639e-04


theta1 =

8.4778e-05


theta2 =

-1.9356e-04


theta1 =

6.4073e-05


theta2 =

-2.0900e-04


theta1 =

9.1034e-05


theta2 =

-3.3095e-04


theta1 =

9.0072e-05


theta2 =

-3.2686e-04


theta1 =

4.0393e-05


theta2 =

-1.3347e-04


theta1 =

2.9739e-05


theta2 =

-1.1183e-04


theta1 =

2.6355e-05


theta2 =

-1.0134e-04


theta1 =

1.1126e-05


theta2 =

-7.3968e-05


theta1 =

1.1944e-05


theta2 =

-1.0895e-04


theta1 =

1.2354e-05


theta2 =

-1.0922e-04


theta1 =

6.4571e-06


theta2 =

-4.4182e-05


theta1 =

3.0912e-06


theta2 =

-3.2179e-05


theta1 =

2.4370e-06


theta2 =

-2.8491e-05


theta1 =

-2.8246e-06


theta2 =

-1.0621e-05


theta1 =

-6.5275e-06


theta2 =

-9.0795e-06


theta1 =

-6.4233e-06


theta2 =

-9.0354e-06


theta1 =

-1.9218e-06


theta2 =

-6.4269e-06


theta1 =

-2.5009e-06


theta2 =

-1.8321e-06


theta1 =

-2.3247e-06


theta2 =

-1.2878e-06


theta1 =

-3.7346e-06


theta2 =

6.2077e-06


theta1 =

-7.4130e-06


theta2 =

1.4059e-05


theta1 =

-7.4058e-06


theta2 =

1.3402e-05


theta1 =

-1.8767e-06


theta2 =

3.2088e-06


theta1 =

-1.5020e-06


theta2 =

3.4851e-06


theta1 =

-1.2784e-06


theta2 =

2.9590e-06


theta1 =

-1.4988e-06


theta2 =

5.7454e-06


theta1 =

-3.9451e-06


theta2 =

1.4958e-05


theta1 =

-4.5014e-06


theta2 =

1.5803e-05


theta1 =

-3.5323e-07


theta2 =

1.5406e-06


theta1 =

-7.7812e-08


theta2 =

7.8301e-07


theta1 =

-9.2471e-08


theta2 =

6.2266e-07


theta1 =

3.5922e-07


theta2 =

1.3426e-06


theta1 =

7.1504e-07


theta2 =

6.3133e-06


theta1 =

-2.1527e-07


theta2 =

1.0386e-05


theta1 =

2.0013e-07


theta2 =

-3.6183e-07


theta1 =

1.3924e-07


theta2 =

-3.8776e-07


theta1 =

1.0388e-07


theta2 =

-2.6309e-07


theta1 =

3.3345e-07


theta2 =

-1.4017e-06


theta1 =

1.2531e-06


theta2 =

-4.7996e-06


theta1 =

1.6482e-06


theta2 =

-5.5142e-06


theta1 =

-5.9195e-10


theta2 =

-1.3294e-07


theta1 =

-2.7180e-08


theta2 =

1.1614e-09


theta1 =

-1.0301e-08


theta2 =

-2.3966e-08


theta1 =

-2.2013e-07


theta2 =

3.3427e-07


theta1 =

-7.3920e-07


theta2 =

8.5005e-07


theta1 =

-7.4437e-07


theta2 =

2.5184e-07


theta1 =

-4.6910e-08


theta2 =

1.6898e-07


theta1 =

-1.2614e-08


theta2 =

9.0900e-08


theta1 =

-1.3294e-08


theta2 =

6.4180e-08


theta1 =

7.9522e-09


theta2 =

3.5303e-07


theta1 =

-7.4665e-08


theta2 =

1.5535e-06


theta1 =

-3.0255e-07


theta2 =

2.3788e-06


theta1 =

3.9125e-08


theta2 =

-5.5921e-08

>>


theta1 =

0


theta2 =

5


theta1 =

4.0190e-05


theta2 =

4.9998


theta1 =

6.0283e-05


theta2 =

4.9997


theta1 =

1.6075e-04


theta2 =

4.9992


theta1 =

1.7861e-04


theta2 =

4.9991


theta1 =

2.0093e-04


theta2 =

4.9990


theta1 =

2.0093e-04


theta2 =

4.9990


theta1 =

4.0184e-04


theta2 =

4.9980


theta1 =

5.0225e-04


theta2 =

4.9975


theta1 =

0.0010


theta2 =

4.9950


theta1 =

0.0011


theta2 =

4.9945


theta1 =

0.0012


theta2 =

4.9940


theta1 =

0.0012


theta2 =

4.9940


theta1 =

0.0022


theta2 =

4.9890


theta1 =

0.0027


theta2 =

4.9864


theta1 =

0.0052


theta2 =

4.9739


theta1 =

0.0057


theta2 =

4.9717


theta1 =

0.0062


theta2 =

4.9689


theta1 =

0.0062


theta2 =

4.9689


theta1 =

0.0112


theta2 =

4.9439


theta1 =

0.0137


theta2 =

4.9315


theta1 =

0.0260


theta2 =

4.8694


theta1 =

0.0282


theta2 =

4.8584


theta1 =

0.0309


theta2 =

4.8447


theta1 =

0.0309


theta2 =

4.8447


theta1 =

0.0552


theta2 =

4.7215


theta1 =

0.0667


theta2 =

4.6621


theta1 =

0.1235


theta2 =

4.3667


theta1 =

0.1333


theta2 =

4.3151


theta1 =

0.1453


theta2 =

4.2516


theta1 =

0.1450


theta2 =

4.2520


theta1 =

0.2518


theta2 =

3.6824


theta1 =

0.2891


theta2 =

3.4491


theta1 =

0.4808


theta2 =

2.2964


theta1 =

0.5301


theta2 =

2.0758


theta1 =

0.5568


theta2 =

1.8717


theta1 =

0.5228


theta2 =

1.9337


theta1 =

0.6436


theta2 =

1.0237


theta1 =

0.6400


theta2 =

0.8190


theta1 =

0.8292


theta2 =

-0.7364


theta1 =

1.1781


theta2 =

-1.8576


theta1 =

1.1753


theta2 =

-2.0565


theta1 =

0.6460


theta2 =

-0.5724


theta1 =

0.6017


theta2 =

1.3396


theta1 =

0.6138


theta2 =

1.1489


theta1 =

0.7215


theta2 =

0.0939


theta1 =

0.8150


theta2 =

-0.2814


theta1 =

0.8140


theta2 =

-0.4169


theta1 =

0.6838


theta2 =

-0.0614


theta1 =

0.6813


theta2 =

-0.3016


theta1 =

0.6690


theta2 =

-0.3658


theta1 =

0.6360


theta2 =

-0.7659


theta1 =

0.6729


theta2 =

-0.9706


theta1 =

0.6562


theta2 =

-1.0073


theta1 =

0.5844


theta2 =

-0.7683


theta1 =

0.5484


theta2 =

-0.8418


theta1 =

0.5266


theta2 =

-0.8435


theta1 =

0.4422


theta2 =

-0.9296


theta1 =

0.4621


theta2 =

-1.0653


theta1 =

0.4413


theta2 =

-1.0520


theta1 =

0.3859


theta2 =

-0.8473


theta1 =

0.3412


theta2 =

-0.8186


theta1 =

0.3206


theta2 =

-0.7885


theta1 =

0.2342


theta2 =

-0.7068


theta1 =

0.2412


theta2 =

-0.7929


theta1 =

0.2257


theta2 =

-0.7629


theta1 =

0.1921


theta2 =

-0.5998


theta1 =

0.1605


theta2 =

-0.5404


theta1 =

0.1482


theta2 =

-0.5102


theta1 =

0.0911


theta2 =

-0.3925


theta1 =

0.0861


theta2 =

-0.4181


theta1 =

0.0780


theta2 =

-0.3947


theta1 =

0.0718


theta2 =

-0.3226


theta1 =

0.0554


theta2 =

-0.2766


theta1 =

0.0499


theta2 =

-0.2575


theta1 =

0.0215


theta2 =

-0.1719


theta1 =

0.0147


theta2 =

-0.1686


theta1 =

0.0113


theta2 =

-0.1551


theta1 =

0.0153


theta2 =

-0.1388


theta1 =

0.0086


theta2 =

-0.1124


theta1 =

0.0066


theta2 =

-0.1028


theta1 =

-0.0045


theta2 =

-0.0553


theta1 =

-0.0091


theta2 =

-0.0466


theta1 =

-0.0100


theta2 =

-0.0402


theta1 =

-0.0054


theta2 =

-0.0426


theta1 =

-0.0073


theta2 =

-0.0306


theta1 =

-0.0077


theta2 =

-0.0267


theta1 =

-0.0104


theta2 =

-0.0060


theta1 =

-0.0124


theta2 =

9.2533e-05


theta1 =

-0.0124


theta2 =

0.0025


theta1 =

-0.0098


theta2 =

-0.0023


theta1 =

-0.0099


theta2 =

0.0027


theta1 =

-0.0097


theta2 =

0.0040


theta1 =

-0.0094


theta2 =

0.0120


theta1 =

-0.0105


theta2 =

0.0163


theta1 =

-0.0102


theta2 =

0.0168


theta1 =

-0.0083


theta2 =

0.0117


theta1 =

-0.0077


theta2 =

0.0128


theta1 =

-0.0074


theta2 =

0.0127


theta1 =

-0.0061


theta2 =

0.0139


theta1 =

-0.0065


theta2 =

0.0161


theta1 =

-0.0062


theta2 =

0.0158


theta1 =

-0.0052


theta2 =

0.0124


theta1 =

-0.0046


theta2 =

0.0118


theta1 =

-0.0043


theta2 =

0.0113


theta1 =

-0.0030


theta2 =

0.0099


theta1 =

-0.0032


theta2 =

0.0112


theta1 =

-0.0029


theta2 =

0.0108


theta1 =

-0.0025


theta2 =

0.0083


theta1 =

-0.0020


theta2 =

0.0074


theta1 =

-0.0019


theta2 =

0.0070


theta1 =

-0.0011


theta2 =

0.0052


theta1 =

-0.0010


theta2 =

0.0055


theta1 =

-9.1636e-04


theta2 =

0.0051


theta1 =

-8.7258e-04


theta2 =

0.0043


theta1 =

-6.5761e-04


theta2 =

0.0037


theta1 =

-5.8648e-04


theta2 =

0.0034


theta1 =

-2.1494e-04


theta2 =

0.0022


theta1 =

-1.1612e-04


theta2 =

0.0021


theta1 =

-7.3738e-05


theta2 =

0.0019


theta1 =

-1.4259e-04


theta2 =

0.0018


theta1 =

-5.4799e-05


theta2 =

0.0014


theta1 =

-3.1483e-05


theta2 =

0.0013


theta1 =

1.1057e-04


theta2 =

6.2229e-04


theta1 =

1.7696e-04


theta2 =

4.8492e-04


theta1 =

1.8736e-04


theta2 =

4.0234e-04


theta1 =

1.1366e-04


theta2 =

4.6341e-04


theta1 =

1.3634e-04


theta2 =

2.9543e-04


theta1 =

1.3844e-04


theta2 =

2.4543e-04


theta1 =

1.6819e-04


theta2 =

-3.5719e-05


theta1 =

2.0269e-04


theta2 =

-1.3899e-04


theta1 =

2.0052e-04


theta2 =

-1.6563e-04


theta1 =

1.5095e-04


theta2 =

-6.6244e-05


theta1 =

1.4739e-04


theta2 =

-1.2796e-04


theta1 =

1.4189e-04


theta2 =

-1.3808e-04


theta1 =

1.3001e-04


theta2 =

-2.2969e-04


theta1 =

1.5061e-04


theta2 =

-3.0808e-04


theta1 =

1.4520e-04


theta2 =

-3.0809e-04


theta1 =

1.0836e-04


theta2 =

-2.0253e-04


theta1 =

9.2861e-05


theta2 =

-2.0639e-04


theta1 =

8.4778e-05


theta2 =

-1.9356e-04


theta1 =

6.4073e-05


theta2 =

-2.0900e-04


theta1 =

9.1034e-05


theta2 =

-3.3095e-04


theta1 =

9.0072e-05


theta2 =

-3.2686e-04


theta1 =

4.0393e-05


theta2 =

-1.3347e-04


theta1 =

2.9739e-05


theta2 =

-1.1183e-04


theta1 =

2.6355e-05


theta2 =

-1.0134e-04


theta1 =

1.1126e-05


theta2 =

-7.3968e-05


theta1 =

1.1944e-05


theta2 =

-1.0895e-04


theta1 =

1.2354e-05


theta2 =

-1.0922e-04


theta1 =

6.4571e-06


theta2 =

-4.4182e-05


theta1 =

3.0912e-06


theta2 =

-3.2179e-05


theta1 =

2.4370e-06


theta2 =

-2.8491e-05


theta1 =

-2.8246e-06


theta2 =

-1.0621e-05


theta1 =

-6.5275e-06


theta2 =

-9.0795e-06


theta1 =

-6.4233e-06


theta2 =

-9.0354e-06


theta1 =

-1.9218e-06


theta2 =

-6.4269e-06


theta1 =

-2.5009e-06


theta2 =

-1.8321e-06


theta1 =

-2.3247e-06


theta2 =

-1.2878e-06


theta1 =

-3.7346e-06


theta2 =

6.2077e-06


theta1 =

-7.4130e-06


theta2 =

1.4059e-05


theta1 =

-7.4058e-06


theta2 =

1.3402e-05


theta1 =

-1.8767e-06


theta2 =

3.2088e-06


theta1 =

-1.5020e-06


theta2 =

3.4851e-06


theta1 =

-1.2784e-06


theta2 =

2.9590e-06


theta1 =

-1.4988e-06


theta2 =

5.7454e-06


theta1 =

-3.9451e-06


theta2 =

1.4958e-05


theta1 =

-4.5014e-06


theta2 =

1.5803e-05


theta1 =

-3.5323e-07


theta2 =

1.5406e-06


theta1 =

-7.7812e-08


theta2 =

7.8301e-07


theta1 =

-9.2471e-08


theta2 =

6.2266e-07


theta1 =

3.5922e-07


theta2 =

1.3426e-06


theta1 =

7.1504e-07


theta2 =

6.3133e-06


theta1 =

-2.1527e-07


theta2 =

1.0386e-05


theta1 =

2.0013e-07


theta2 =

-3.6183e-07


theta1 =

1.3924e-07


theta2 =

-3.8776e-07


theta1 =

1.0388e-07


theta2 =

-2.6309e-07


theta1 =

3.3345e-07


theta2 =

-1.4017e-06


theta1 =

1.2531e-06


theta2 =

-4.7996e-06


theta1 =

1.6482e-06


theta2 =

-5.5142e-06


theta1 =

-5.9195e-10


theta2 =

-1.3294e-07


theta1 =

-2.7180e-08


theta2 =

1.1614e-09


theta1 =

-1.0301e-08


theta2 =

-2.3966e-08


theta1 =

-2.2013e-07


theta2 =

3.3427e-07


theta1 =

-7.3920e-07


theta2 =

8.5005e-07


theta1 =

-7.4437e-07


theta2 =

2.5184e-07


theta1 =

-4.6910e-08


theta2 =

1.6898e-07


theta1 =

-1.2614e-08


theta2 =

9.0900e-08


theta1 =

-1.3294e-08


theta2 =

6.4180e-08


theta1 =

7.9522e-09


theta2 =

3.5303e-07


theta1 =

-7.4665e-08


theta2 =

1.5535e-06


theta1 =

-3.0255e-07


theta2 =

2.3788e-06


theta1 =

3.9125e-08


theta2 =

-5.5921e-08

>>

Your portfolio, next

Ship work like this
in your own course.

Talk to a career counsellor

Free 20-minute call. We'll map the right course to where you want to work.

By submitting you agree to our Terms and Privacy Policy.