Eqn1:=diff(u(t),t$2)+(1/8)*diff(u(t),t)+4*u(t)=Ft;

DE21:=subs(Ft=3*cos(t/4),Eqn1);

DE22:=subs(Ft=3*cos(2*t),Eqn1);

DE23:=subs(Ft=3*cos(6*t),Eqn1);

#Exercise 21:

U21:=rhs(dsolve({DE21,u(0)=2,D(u)(0)=0},u(t)));

dU21:=diff(U21,t);

#Part (a): Plot the forcing and the solution together:

plot({3*cos(t/4),U21},t=0..36*Pi);

#Part (b): Plot (x(t)=u(t),y(t)=u'(t))- This is a parametric plot.

plot([U21,dU21,t=0..36*Pi]);

#Exercise 22:

U22:=rhs(dsolve({DE22,u(0)=2,D(u)(0)=0},u(t)));

dU22:=diff(U22,t);

#Part (a): Plot the forcing and the solution together:

plot({3*cos(2*t),U22},t=0..20*Pi);

#Part (b): Plot (x(t)=u(t),y(t)=u'(t))- This is a parametric plot.

plot([U22,dU22,t=0..20*Pi]);

#Exercise 23:

U23:=rhs(dsolve({DE23,u(0)=2,D(u)(0)=0},u(t)));

dU23:=diff(U23,t);

#Part (a): Plot the forcing and the solution together:

plot({3*cos(6*t),U23},t=0..10*Pi);

#Part (b): Plot (x(t)=u(t),y(t)=u'(t))- This is a parametric plot.

plot([U23,dU23,t=0..36*Pi]);