Question

Modify - SecondOrder ODE.m to do the following a) Use the ode450 function to plot the solution for: x+4ä+ 6x +8x - f(t) where f(t) - u(t) (a unit step) over the range 0 to 10 seconds. All initial conditions are zero. Plot the position and velocity on separate graphs

modify this code is ready

% Use ODE45 to solve Example 4.4.3, page 205, Palm 3rd edition

% Spring Mass Damper system with initial displacement

function SolveODEs()

clf %clear any existing plots

% Time range Initial Conditions

[t,y] = ode45( @deriv, [0,2], [1,0] );

% tvals yvals color and style

plot( t, y(:,1), 'blue');

title('Spring Mass Damper with initial displacement');

xlabel('Time - s');

ylabel('Position - ft');

pause % hit enter to go to the next plot

plot( t, y(:,2), 'blue--');

title('Spring Mass Damper with initial displacement');

xlabel('Time - s');

ylabel('Velocit - ft/s');

pause % hit enter to go to the next plot

plot( t, y(:,1), 'g', t, y(:,2), 'b--');

title('Spring Mass Damper with initial displacement');

xlabel('Time - s');

ylabel('Position and Velocity');

function XDOT = deriv( t, X)

% ind. var dep. var

%define model parameters

m=1; c=4; k=16;

%define the states as "nice" names

x=X(1); xdot=X(2);

%define any forcing functions

f=5*sin(2*t);

%write the non-trivial equations using the nice names

xddot= (1/m) * ( f -c*xdot - k*x );

XDOT = [xdot;xddot] ; %return the derivative value

Answer 1

clear
clc
[t,x]=ode45(@deriv,[0,10],[0,0,0]);
plot(t,x(:,1));
title('position')
figure
plot(t,x(:,2))
title('Velocity')

function XDOT = deriv(t,X)
% ind. var dep. var
x=X(1);
xdot=X(2);
xddot=X(3);
%write the non-trivial equations using the nice names
xtdot= -4*xddot-6*xdot-8*x+u(x);%u(x) is unit step function defined below
XDOT = [xdot;xddot;xtdot] ; %return the derivative value
end
function f=u(t)
if t>=0
     f=1;
else
     f=0;
end
end