Damped Forced Vibration Example

From the End of the Chapter Four Notes and Examples

Here are some Maple commands to solve this problem.

Solution and Graphs:  Solution in orange, steady-state solution in green, transient solution in blue

>	ode:=diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=2*cos(t);

>	dsolve(ode,y(t));

>	ic:=y(0)=0,D(y)(0)=0;

>	dsolve({ode,ic},{y(t)});

>	f:=rhs(%);

>	with(plots):

>	solution:=plot(f,t=0..6*Pi,y=-1..1,color=orange,thickness=2,labels=[t,y]):

>	transient:=plot((4/5)*exp(-2*t)-exp(-t),t=0..6*Pi,y=-1..1,color=blue,thickness=2,labels=[t,y]):

>	steady:=plot((1/5)*cos(t)+(3/5)*sin(t),t=0..6*Pi,y=-1..1,color=green,thickness=2,labels=[t,y]):

>	display(solution,transient,steady);

>