clear
clc
close all
%% defination
m= 750; % mass of the system in kg
k= 50000; % Stiffness of system in N/m
c= 1000; % damping coefficient Ns/m
time= 0:0.01:1; %time in sec
x_0=0.01; % displacement intial condition
x_dot_0= 0; % velocity initial condition
y_0=0.01; % displacement intial condition
y_dot_0= 0; % velocity initial condition
syms x(t)
syms y(t)
D1x= diff(x,1);
D2x= diff(x,2);
D1y= diff(y,1);
D2y= diff(y,2);
%% computing
x= dsolve(m*D2x+k*x==0,x(0)==x_0, D1x(0)==x_dot_0,'t');
y= dsolve(m*D2y+k*y+c*D1y==0,y(0)==y_0, D1y(0)==y_dot_0,'t');
x_fun=matlabFunction(x) % to save solved function values
x_dot_fun = matlabFunction(diff(x))
y_fun=matlabFunction(y)
y_dot_fun = matlabFunction(diff(y))
x_t=x_fun(time);
y_t=y_fun(time);
u_t=x_dot_fun(time);
v_t=y_dot_fun(time);
difference=x_fun(t)-y_fun(t)
%% plotting
% plot parameters
clr=[236/255 237/255 237/255]; % standarad RGB code
unts='normalized'; % Screen resolution percentage
lnwidth=2; % line width of the plot
fnts=22; % font size in percent
pos_fig=[0.01 .1 0.98 0.8];
title_graph='Displacement and velocity vs time';
xlabel_graph='time' ;
ylabel_graph(1)='dispalcement';
ylabel_graph(2)='velocity';
%% plotting
fig= figure('colour',clr,'units',unts,'position',pos_fig);
[axes_graph, Line1,Line2] = plotyy(time,x_t,time,v_t);
