%% ************************************%
% Middle East Technical University %
% Department of Mathematics %
% Date: 28.03.2020 %
% Author: Bakican Ayna %
% Number: 2147627 %
%**************************************%
%% ***********************************************************************%
% PLOTS
close all;
set(groot, 'defaultTextInterpreter','latex')
set(groot, 'defaultAxesTickLabelInterpreter','latex');
set(groot, 'defaultLegendInterpreter','latex');
set(0,'defaultFigureUnits','normalized',...
'defaultFigurePosition',[0 0 1 1])
set(0,'defaultLegendFontSizeMode','manual',...
'defaultLegendFontSize',12,...
'defaultErrorBarMarkerSize',12,...
'defaultErrorBarLineWidth',2,...
'defaultLineMarkerSize',12,...
'defaultLineLineWidth',2,...
'defaultAxesFontSize',14)
%% Trajectories for the Simple Pendulum
C = 3.5;
x = linspace(-5*pi,5*pi,10000);
figure (1)
% Case 2 (w^2 = -C)
subplot(221)
y21 = -sqrt(2*(C-C*cos(x)));
y22 = +sqrt(2*(C-C*cos(x)));
plot(x, y21, 'LineWidth', 1.5,'Color',[0,0.5,0.9]); hold on;
plot(x, y22, 'LineWidth', 1.5,'Color',[0,0.5,0.9]); hold on;
xlim([-16 16])
ylim([-20 20])
ylabel('y');
xlabel('x');
title('C = $-\omega^2$');
% Case 3 (-w^2 < C < w^2)
subplot(222)
% w = 2
y31 = -sqrt(2*(C+(2)^2*cos(x)));
y32 = +sqrt(2*(C+(2)^2*cos(x)));
plot(x, y31, 'LineWidth', 1.5,'Color',[0,0.5,0.9],...
'HandleVisibility','off'); hold on;
plot(x, y32, 'LineWidth', 1.5,'Color',[0,0.5,0.9]); hold on;
