function springmass (p,omega0,y0,v0,tf)

function springmass (p,omega0,y0,v0,tf)

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%springmass(p,omega0,y0,v0,tf,omega) solves the damped harmonic problems

%  y” + 2 p y’ + omega0^2 y = 0

%   with y(t=0)=y0, y'(t=0)=v0 from t=0 to tf using fourth-order Runge-Kutta

t0 = 0;

tspan = [t0 tf];

w0 = [y0; v0];

opts = odeset(‘RelTol’,10^-9,’AbsTol’,10^-12);

[t,w] = ode45(@f,tspan,w0,opts);

figure

plot(t,w(:,1),’b-‘)

xlabel(‘t’,’FontSize’,16)

ylabel(‘y’,’FontSize’,16)

xlim([t0 tf])

function wprime = f(t,w)

wprime = [w(2); -omega0^2*w(1)-2*p*w(2)];

end

end

function springmassdriven(p,omega0,y0,v0,tf,omega)

%springmassdriven(p,omega0,y0,v0,tf,omega) solves the forced damped

%harmonic problems

% y” + 2 p y’ + omega0^2 y = cos(omega t)

%   with y(t=0)=y0, y'(t=0)=v0 from t=0 to tf using fourth-order Runge-Kutta

t0 = 0;

tspan = [t0 tf];

w0 = [y0; v0];

opts = odeset(‘RelTol’,10^-9,’AbsTol’,10^-12);

[t,w] = ode45(@f,tspan,w0,opts);

figure

plot(t,w(:,1),’b-‘)

xlabel(‘t’,’FontSize’,16)

ylabel(‘y’,’FontSize’,16)

xlim([t0 tf])

function wprime = f(t,w)

wprime = [w(2); -omega0^2*w(1)-2*p*w(2)+cos(omega*t)];

end

end