MATLAB program to simulate the Motion Of a Simple Pendulum using 2nd order ODEs.
AIM:- Write a program in Matlab that will simulate the pendulum motion.
THEORY:-
1)Pendulum:-A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.
2)Differential Equation:-In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. For example,
(d^2x/dy^2)+(dx/dy)3−3x+2y=8
3) Simple harmonic motion:-Oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position.
Pendulum Equation:-
a) b=It is a dimensionless measure describing how oscillations in a system decay after a disturbance.
b)θ= It is the angular displacement .Angular displacement of a body is the angle in radians through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis.
c)g=It is the acceleration due to gravity. SI unit is m/s^2.
d)L=Length of string of a pendulum. Its measured in m.
e)m= Mass of bob. Measured in kg.
CODE INPUT:-
a) CODE 1 :-
Before we solve our differential equation, it is important to define it. As MATLAB cannot solve a 2nd order ODE, we have to absolve the ODE into two 1st order ODEs. We need to do this as we have to call this function to solve the ODE. The function is defined as follows:
function [dtheta_dt]=odes(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];
endExplanation:
1)Function command is used to define the fucntion odes.
2)[dtheta_dt] is the output variable and (t,theta,b,g,L,m) are in input arguments.
3)dtheta1_dt=theta2 is the first 1st order ODE.
4)dtheta2_dt= - (b/m)*theta2 - (g/L)*sin(theta1) is the second 1st order ODE.
CODE OUTPUT 1:-
>> odes
Not enough input arguments.It gives an error of 'Not enough input arguments'. It is so because you have to use it in a different program that contain the input values.
b) CODE 2:-
clear all
close all
clc
%Input Data
%Damping Coefficient:-
b=0.05
%Acceleration due to gravity
g=9.81
%Length of String
L=1
%Mass of Bob
m=0.1
%Inital Condition
Initial_cond=[0;3];
%Time Range
t_span=linspace(0,20,100);
%Solution for ODE
[t,results]=ode45(@(t,theta) odes(t,theta,b,g,L,m), t_span,Initial_cond);
plot(t,results(:,1));
hold on
plot(t,results(:,2));
xlabel('time')
ylabel('Plot')
grid on
%Animation
figure
ct=1;
for i=1:length(t)
%Starting point of string
x0=0;
y0=0;
%Coordinates of Bob or endpoint of string
x1=L*sin(results(i,1));
y1=-L*cos(results(i,1));
%Plotting of bob, string and beam
plot([x0 x1],[y0 y1],'color','r');
line([-1 1],[0 0],'linewidth',3,'color','g')
hold on
plot(x1,y1,'marker','o','markersize',25)
axis([-2 2 -1.5 1.5])
grid on
pause(0.03)
N(ct)=getframe(gcf)
ct=ct+1;
hold off
end
movie(N)
videofile=VideoWriter('odes.avi','Uncompressed AVI')
open(videofile)
writeVideo(videofile,N)
close(videofile)
Explantion:-
1)% fucntion creates comments to help signify the important parameter.
2)Value of g,L,b,m are given. Intial condition is an array in which the first row shows the inital angular displacement and second row shows the intital angular velocity. A new row is created using the ';' operator.
3)linspace command is used to denote the time range. It gives the specified no. of vales between a starting and ending value.
4)ode45 is the ODE solver used in this program.
5)plot command is used to to draw a line or graph with the help of coordinates.
6)xlabel and ylabel are used to represent the x axis and y axis respectively.
7)color fucntion is used to assign color to a particular plot or line.
8)linewidth is used to assign the width of the line or plot.
9)hold on command is used to merge the previous plot with the next plot.
10)hold off command is used to terminate the merging of plots.
11)grid on command enables the grid.
12)marker operator is used to generate a marker figure in plot.
13)axis command is used to assign the coordinate system.
14)ct is the counter command.
15)for loop is used to calculate all the value of the time range to determine the position of the bob with repsect to time.
16)getframe captures the current axes as it appears on the screen as a movie frame.
17)gcf creates a figure and returns its handle.
18)movie plays the movie.
19)VideoWriter is used to create a video file from an array or MATLAB movie.
20)writeVideo( v , img ) writes data from an array to the video file associated with v.
CODE OUTPUT 2:-
0.5924
theta2 =
-1.8283
theta1 =
0.4893
theta2 =
-2.0854
theta1 =
0.4215
theta2 =
-2.1509
theta1 =
0.1275
theta2 =
-2.2754
theta1 =
0.1182
theta2 =
-2.0888
theta1 =
0.0319
theta2 =
-2.0451
theta1 =
-0.0300
theta2 =
-2.3011
theta1 =
-0.1550
theta2 =
-2.2226
theta1 =
-0.2127
theta2 =
-2.1112
theta1 =
-0.4262
theta2 =
-1.5605
theta1 =
-0.3846
theta2 =
-1.4527
theta1 =
-0.4320
theta2 =
-1.2546
theta1 =
-0.5380
theta2 =
-1.2461
theta1 =
-0.6013
theta2 =
-0.9588
theta1 =
-0.6166
theta2 =
-0.7934
theta1 =
-0.6549
theta2 =
-0.0779
theta1 =
-0.6224
theta2 =
-0.0675
theta1 =
-0.6148
theta2 =
0.1208
theta1 =
-0.6608
theta2 =
0.2884
theta1 =
-0.6458
theta2 =
0.5949
theta1 =
-0.6203
theta2 =
0.7322
theta1 =
-0.4875
theta2 =
1.2761
theta1 =
-0.4587
theta2 =
1.2286
theta1 =
-0.4099
theta2 =
1.3372
theta1 =
-0.4092
theta2 =
1.5220
theta1 =
-0.3265
theta2 =
1.6927
theta1 =
-0.2747
theta2 =
1.7266
theta1 =
-0.0539
theta2 =
1.7605
theta1 =
-0.0523
theta2 =
1.6223
theta1 =
0.0111
theta2 =
1.5754
theta1 =
0.0647
theta2 =
1.7512
theta1 =
0.1549
theta2 =
1.6734
theta1 =
0.1955
theta2 =
1.5858
theta1 =
0.3489
theta2 =
1.1595
theta1 =
0.3238
theta2 =
1.0894
theta1 =
0.3561
theta2 =
0.9420
theta1 =
0.4251
theta2 =
0.9170
theta1 =
0.4718
theta2 =
0.6877
theta1 =
0.4820
theta2 =
0.5559
theta1 =
0.5030
theta2 =
-0.0079
theta1 =
0.4751
theta2 =
-0.0093
theta1 =
0.4668
theta2 =
-0.1588
theta1 =
0.5041
theta2 =
-0.2993
theta1 =
0.4891
theta2 =
-0.5286
theta1 =
0.4688
theta2 =
-0.6295
theta1 =
0.3648
theta2 =
-1.0249
theta1 =
0.3442
theta2 =
-0.9836
theta1 =
0.3071
theta2 =
-1.0612
theta1 =
0.3044
theta2 =
-1.2044
theta1 =
0.2407
theta2 =
-1.3282
theta1 =
0.2014
theta2 =
-1.3506
theta1 =
0.0341
theta2 =
-1.3667
theta1 =
0.0335
theta2 =
-1.2671
theta1 =
-0.0139
theta2 =
-1.2300
theta1 =
-0.0554
theta2 =
-1.3538
theta1 =
-0.1239
theta2 =
-1.2920
theta1 =
-0.1547
theta2 =
-1.2247
theta1 =
-0.2718
theta2 =
-0.8967
theta1 =
-0.2541
theta2 =
-0.8435
theta1 =
-0.2785
theta2 =
-0.7305
theta1 =
-0.3291
theta2 =
-0.7101
theta1 =
-0.3651
theta2 =
-0.5317
theta1 =
-0.3729
theta2 =
-0.4286
theta1 =
-0.3882
theta2 =
0.0107
theta1 =
-0.3659
theta2 =
0.0104
theta1 =
-0.3593
theta2 =
0.1279
theta1 =
-0.3891
theta2 =
0.2390
theta1 =
-0.3773
theta2 =
0.4160
theta1 =
-0.3617
theta2 =
0.4937
theta1 =
-0.2820
theta2 =
0.7965
theta1 =
-0.2663
theta2 =
0.7621
theta1 =
-0.2379
theta2 =
0.8217
theta1 =
-0.2358
theta2 =
0.9354
theta1 =
-0.1871
theta2 =
1.0302
theta1 =
-0.1573
theta2 =
1.0475
theta1 =
-0.0296
theta2 =
1.0636
theta1 =
-0.0287
theta2 =
0.9906
theta1 =
0.0073
theta2 =
0.9638
theta1 =
0.0385
theta2 =
1.0550
theta1 =
0.0918
theta2 =
1.0093
theta1 =
0.1159
theta2 =
0.9581
theta1 =
0.2078
theta2 =
0.7067
theta1 =
0.1944
theta2 =
0.6646
theta1 =
0.2137
theta2 =
0.5772
theta1 =
0.2527
theta2 =
0.5633
theta1 =
0.2810
theta2 =
0.4259
theta1 =
0.2874
theta2 =
0.3460
theta1 =
0.3007
theta2 =
0.0048
theta1 =
0.2833
theta2 =
0.0044
theta1 =
0.2786
theta2 =
-0.0874
theta1 =
0.3022
theta2 =
-0.1730
theta1 =
0.2937
theta2 =
-0.3117
theta1 =
0.2819
theta2 =
-0.3729
theta1 =
0.2211
theta2 =
-0.6105
theta1 =
0.2089
theta2 =
-0.5822
theta1 =
0.1870
theta2 =
-0.6295
theta1 =
0.1858
theta2 =
-0.7208
theta1 =
0.1489
theta2 =
-0.7953
theta1 =
0.1261
theta2 =
-0.8098
theta1 =
0.0282
theta2 =
-0.8283
theta1 =
0.0270
theta2 =
-0.7741
theta1 =
-6.1608e-04
theta2 =
-0.7555
theta1 =
-0.0240
theta2 =
-0.8245
theta1 =
-0.0657
theta2 =
-0.7917
theta1 =
-0.0848
theta2 =
-0.7528
theta1 =
-0.1576
theta2 =
-0.5608
theta1 =
-0.1472
theta2 =
-0.5268
theta1 =
-0.1627
theta2 =
-0.4591
theta1 =
-0.1934
theta2 =
-0.4506
theta1 =
-0.2159
theta2 =
-0.3453
theta1 =
-0.2212
theta2 =
-0.2835
theta1 =
-0.2332
theta2 =
-0.0189
theta1 =
-0.2198
theta2 =
-0.0175
theta1 =
-0.2167
theta2 =
0.0541
theta1 =
-0.2353
theta2 =
0.1193
theta1 =
-0.2295
theta2 =
0.2285
theta1 =
-0.2205
theta2 =
0.2771
theta1 =
-0.1743
theta2 =
0.4653
theta1 =
-0.1645
theta2 =
0.4422
theta1 =
-0.1477
theta2 =
0.4803
theta1 =
-0.1473
theta2 =
0.5539
theta1 =
-0.1192
theta2 =
0.6129
theta1 =
-0.1018
theta2 =
0.6251
theta1 =
-0.0265
theta2 =
0.6449
theta1 =
-0.0252
theta2 =
0.6042
theta1 =
-0.0039
theta2 =
0.5915
theta1 =
0.0135
theta2 =
0.6445
theta1 =
0.0463
theta2 =
0.6213
theta1 =
0.0614
theta2 =
0.5919
theta1 =
0.1193
theta2 =
0.4452
theta1 =
0.1112
theta2 =
0.4178
theta1 =
0.1236
theta2 =
0.3652
theta1 =
0.1479
theta2 =
0.3606
theta1 =
0.1658
theta2 =
0.2800
theta1 =
0.1703
theta2 =
0.2323
theta1 =
0.1809
theta2 =
0.0272
theta1 =
0.1707
theta2 =
0.0252
theta1 =
0.1687
theta2 =
-0.0306
theta1 =
0.1833
theta2 =
-0.0800
theta1 =
0.1794
theta2 =
-0.1662
theta1 =
0.1726
theta2 =
-0.2047
theta1 =
0.1375
theta2 =
-0.3542
theta1 =
0.1297
theta2 =
-0.3355
theta1 =
0.1166
theta2 =
-0.3662
theta1 =
0.1169
theta2 =
-0.4253
theta1 =
0.0955
theta2 =
-0.4722
theta1 =
0.0821
theta2 =
-0.4824
theta1 =
0.0241
theta2 =
-0.5018
theta1 =
0.0228
theta2 =
-0.4710
theta1 =
0.0064
theta2 =
-0.4624
theta1 =
-0.0067
theta2 =
-0.5034
theta1 =
-0.0325
theta2 =
-0.4871
theta1 =
-0.0445
theta2 =
-0.4649
theta1 =
-0.0904
theta2 =
-0.3527
theta1 =
-0.0840
theta2 =
-0.3306
theta1 =
-0.0940
theta2 =
-0.2899
theta1 =
-0.1133
theta2 =
-0.2877
theta1 =
-0.1274
theta2 =
-0.2260
theta1 =
-0.1311
theta2 =
-0.1891
theta1 =
-0.1404
theta2 =
-0.0302
theta1 =
-0.1326
theta2 =
-0.0280
theta1 =
-0.1313
theta2 =
0.0154
theta1 =
-0.1428
theta2 =
0.0529
theta1 =
-0.1402
theta2 =
0.1207
theta1 =
-0.1351
theta2 =
0.1513
theta1 =
-0.1083
theta2 =
0.2698
theta1 =
-0.1021
theta2 =
0.2548
theta1 =
-0.0920
theta2 =
0.2795
theta1 =
-0.0925
theta2 =
0.3267
theta1 =
-0.0762
theta2 =
0.3639
theta1 =
-0.0659
theta2 =
0.3725
theta1 =
-0.0212
theta2 =
0.3902
theta1 =
-0.0200
theta2 =
0.3668
theta1 =
-0.0073
theta2 =
0.3610
theta1 =
0.0026
theta2 =
0.3929
theta1 =
0.0228
theta2 =
0.3814
theta1 =
0.0323
theta2 =
0.3645
theta1 =
0.0686
theta2 =
0.2787
theta1 =
0.0636
theta2 =
0.2609
theta1 =
0.0716
theta2 =
0.2293
theta1 =
0.0868
theta2 =
0.2287
theta1 =
0.0981
theta2 =
0.1813
theta1 =
0.1011
theta2 =
0.1528
theta1 =
0.1090
theta2 =
0.0297
theta1 =
0.1030
theta2 =
0.0276
theta1 =
0.1022
theta2 =
-0.0062
theta1 =
0.1112
theta2 =
-0.0347
theta1 =
0.1095
theta2 =
-0.0880
theta1 =
0.1056
theta2 =
-0.1122
theta1 =
0.0852
theta2 =
-0.2060
theta1 =
0.0802
theta2 =
-0.1940
theta1 =
0.0724
theta2 =
-0.2137
theta1 =
0.0731
theta2 =
-0.2513
theta1 =
0.0606
theta2 =
-0.2807
theta1 =
0.0526
theta2 =
-0.2877
theta1 =
0.0181
theta2 =
-0.3034
theta1 =
0.0170
theta2 =
-0.2855
theta1 =
0.0072
theta2 =
-0.2815
theta1 =
-2.6096e-04
theta2 =
-0.3063
theta1 =
-0.0161
theta2 =
-0.2982
theta1 =
-0.0236
theta2 =
-0.2854
theta1 =
-0.0522
theta2 =
-0.2195
theta1 =
-0.0483
theta2 =
-0.2053
theta1 =
-0.0547
theta2 =
-0.1808
theta1 =
-0.0667
theta2 =
-0.1811
theta1 =
-0.0756
theta2 =
-0.1446
theta1 =
-0.0780
theta2 =
-0.1226
theta1 =
-0.0846
theta2 =
-0.0272
theta1 =
-0.0800
theta2 =
-0.0252
theta1 =
-0.0795
theta2 =
0.0010
theta1 =
-0.0865
theta2 =
0.0227
theta1 =
-0.0854
theta2 =
0.0645
theta1 =
-0.0825
theta2 =
0.0836
theta1 =
-0.0669
theta2 =
0.1576
theta1 =
-0.0629
theta2 =
0.1481
theta1 =
-0.0568
theta2 =
0.1638
theta1 =
-0.0575
theta2 =
0.1936
theta1 =
-0.0479
theta2 =
0.2168
theta1 =
-0.0418
theta2 =
0.2225
theta1 =
-0.0151
theta2 =
0.2358
theta1 =
-0.0142
theta2 =
0.2221
theta1 =
-0.0066
theta2 =
0.2193
theta1 =
-9.2731e-04
theta2 =
0.2387
theta1 =
0.0115
theta2 =
0.2329
theta1 =
0.0174
theta2 =
0.2231
theta1 =
0.0399
theta2 =
0.1725
theta1 =
0.0368
theta2 =
0.1612
theta1 =
0.0419
theta2 =
0.1422
theta1 =
0.0513
theta2 =
0.1429
theta1 =
0.0583
theta2 =
0.1148
theta1 =
0.0603
theta2 =
0.0978
theta1 =
0.0657
theta2 =
0.0238
theta1 =
0.0621
theta2 =
0.0221
theta1 =
0.0619
theta2 =
0.0017
theta1 =
0.0673
theta2 =
-0.0149
theta1 =
0.0666
theta2 =
-0.0477
theta1 =
0.0644
theta2 =
-0.0627
theta1 =
0.0524
theta2 =
-0.1208
theta1 =
0.0492
theta2 =
-0.1134
theta1 =
0.0445
theta2 =
-0.1258
theta1 =
0.0452
theta2 =
-0.1493
theta1 =
0.0378
theta2 =
-0.1675
theta1 =
0.0331
theta2 =
-0.1721
theta1 =
0.0124
theta2 =
-0.1832
theta1 =
0.0117
theta2 =
-0.1727
theta1 =
0.0058
theta2 =
-0.1708
theta1 =
0.0014
theta2 =
-0.1858
theta1 =
-0.0083
theta2 =
-0.1817
theta1 =
-0.0129
theta2 =
-0.1742
theta1 =
-0.0306
theta2 =
-0.1353
theta1 =
-0.0281
theta2 =
-0.1263
theta1 =
-0.0321
theta2 =
-0.1115
theta1 =
-0.0396
theta2 =
-0.1124
theta1 =
-0.0450
theta2 =
-0.0907
theta1 =
-0.0466
theta2 =
-0.0776
theta1 =
-0.0510
theta2 =
-0.0202
theta1 =
-0.0483
theta2 =
-0.0187
theta1 =
-0.0481
theta2 =
-0.0029
theta1 =
-0.0524
theta2 =
0.0098
theta1 =
-0.0519
theta2 =
0.0354
theta1 =
-0.0502
theta2 =
0.0473
theta1 =
-0.0410
theta2 =
0.0929
theta1 =
-0.0385
theta2 =
0.0870
theta1 =
-0.0349
theta2 =
0.0969
theta1 =
-0.0354
theta2 =
0.1153
theta1 =
-0.0298
theta2 =
0.1296
theta1 =
-0.0261
theta2 =
0.1333
theta1 =
-0.0101
theta2 =
0.1424
theta1 =
-0.0095
theta2 =
0.1343
theta1 =
-0.0049
theta2 =
0.1330
theta1 =
-0.0016
theta2 =
0.1447
theta1 =
0.0060
theta2 =
0.1417
theta1 =
0.0096
theta2 =
0.1359
theta1 =
0.0235
theta2 =
0.1059
theta1 =
0.0216
theta2 =
0.0988
theta1 =
0.0247
theta2 =
0.0873
theta1 =
0.0306
theta2 =
0.0882
theta1 =
0.0348
theta2 =
0.0715
theta1 =
0.0361
theta2 =
0.0613
theta1 =
0.0396
theta2 =
0.0168
theta1 =
0.0375
theta2 =
0.0155
theta1 =
0.0374
theta2 =
0.0032
theta1 =
0.0407
theta2 =
-0.0065
theta1 =
0.0404
theta2 =
-0.0266
theta1 =
0.0391
theta2 =
-0.0358
theta1 =
0.0320
theta2 =
-0.0716
theta1 =
0.0301
theta2 =
-0.0669
theta1 =
0.0272
theta2 =
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0.0205
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theta1 =
0.0076
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0.0041
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0.0015
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-0.0127
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-0.0291
theta2 =
-0.0031
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theta2 =
0.0044
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0.0200
theta1 =
-0.0305
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0.0273
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0.0552
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0.0516
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0.0577
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0.0690
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0.0778
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0.0801
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0.0860
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0.0805
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0.0055
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0.0217
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theta2 =
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theta1 =
0.0051
theta2 =
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theta1 =
0.0048
theta2 =
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theta1 =
0.0027
theta2 =
-0.0626
theta1 =
0.0012
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theta1 =
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theta2 =
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theta1 =
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theta1 =
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theta2 =
0.0021
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0.0116
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0.0160
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0.0330
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0.0308
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0.0345
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0.0415
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theta2 =
0.0468
theta1 =
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theta2 =
0.0482
theta1 =
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theta2 =
0.0519
theta1 =
-0.0038
theta2 =
0.0491
theta1 =
-0.0021
theta2 =
0.0487
theta1 =
-9.6003e-04
theta2 =
0.0530
theta1 =
0.0018
theta2 =
0.0521
theta1 =
0.0032
theta2 =
0.0500
theta1 =
0.0083
theta2 =
0.0393
theta1 =
0.0076
theta2 =
0.0366
theta1 =
0.0088
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theta1 =
0.0110
theta2 =
0.0329
theta1 =
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theta2 =
0.0269
theta1 =
0.0130
theta2 =
0.0232
theta1 =
0.0144
theta2 =
0.0070
theta1 =
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theta2 =
0.0065
theta1 =
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theta2 =
0.0020
theta1 =
0.0149
theta2 =
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theta1 =
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theta2 =
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theta1 =
0.0144
theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta1 =
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theta2 =
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theta1 =
0.0077
theta2 =
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theta1 =
0.0032
theta2 =
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theta1 =
0.0030
theta2 =
-0.0381
theta1 =
0.0017
theta2 =
-0.0379
theta1 =
7.8635e-04
theta2 =
-0.0412
theta1 =
-0.0014
theta2 =
-0.0405
theta1 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
-0.0085
theta2 =
-0.0256
theta1 =
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theta2 =
-0.0210
theta1 =
-0.0101
theta2 =
-0.0181
theta1 =
-0.0112
theta2 =
-0.0055
theta1 =
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theta2 =
-0.0051
theta1 =
-0.0106
theta2 =
-0.0017
theta1 =
-0.0116
theta2 =
0.0010
theta1 =
-0.0115
theta2 =
0.0068
theta1 =
-0.0112
theta2 =
0.0095
theta1 =
-0.0092
theta2 =
0.0198
theta1 =
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theta2 =
0.0185
theta1 =
-0.0078
theta2 =
0.0208
theta1 =
-0.0080
theta2 =
0.0250
theta1 =
-0.0068
theta2 =
0.0282
theta1 =
-0.0060
theta2 =
0.0291
theta1 =
-0.0025
theta2 =
0.0314
theta1 =
-0.0023
theta2 =
0.0296
theta1 =
-0.0013
theta2 =
0.0294
theta1 =
-6.3569e-04
theta2 =
0.0320
theta1 =
0.0011
theta2 =
0.0315
theta1 =
0.0019
theta2 =
0.0303
theta1 =
0.0050
theta2 =
0.0238
theta1 =
0.0046
theta2 =
0.0222
theta1 =
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theta2 =
0.0197
theta1 =
0.0066
theta2 =
0.0200
theta1 =
0.0076
theta2 =
0.0164
theta1 =
0.0079
theta2 =
0.0141
theta1 =
0.0087
theta2 =
0.0044
theta1 =
0.0083
theta2 =
0.0041
theta1 =
0.0083
theta2 =
0.0013
theta1 =
0.0090
theta2 =
-7.4688e-04
theta1 =
0.0090
theta2 =
-0.0052
theta1 =
0.0087
theta2 =
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theta1 =
0.0072
theta2 =
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theta1 =
0.0067
theta2 =
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theta1 =
0.0061
theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
0.0047
theta2 =
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theta1 =
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theta2 =
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theta1 =
0.0018
theta2 =
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theta1 =
0.0011
theta2 =
-0.0229
theta1 =
5.0901e-04
theta2 =
-0.0249
theta1 =
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theta2 =
-0.0245
theta1 =
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theta2 =
-0.0236
theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
-0.0059
theta2 =
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theta1 =
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theta2 =
-0.0110
theta1 =
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theta2 =
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theta1 =
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theta2 =
-0.0032
theta1 =
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theta2 =
-0.0011
theta1 =
-0.0070
theta2 =
5.4486e-04
theta1 =
-0.0070
theta2 =
0.0043
theta1 =
-0.0067
theta2 =
0.0061
theta1 =
-0.0053
theta2 =
0.0125
theta1 =
-0.0049
theta2 =
0.0112
theta1 =
-0.0043
theta2 =
0.0126
theta1 =
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theta2 =
0.0159
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videofile =
VideoWriter
General Properties:
Filename: 'odes.avi'
Path: 'C:UsersDELL'
FileFormat: 'avi'
Duration: 0
Video Properties:
ColorChannels: 3
Height: []
Width: []
FrameCount: 0
FrameRate: 30
VideoBitsPerPixel: 24
VideoFormat: 'RGB24'
VideoCompressionMethod: 'None'
Methods
>> Explanation:-
The output shows a plot and also the video file is created.
PLOT:-
Here, the blue line represents the displacement as the initial value was 0. The red line represents velocity as the inital value was 3 rad/s
Result:-
After assigning the values of all the variables and properly executing the functions, we see that a resultant plot is generated between the values of velocity and displacement with respect to time. Also a video file showing the animation of the motion of simple pendulum is created.
Video file link:-
YOUTUBE:- https://youtu.be/91HFxkv-J00