@Carl Love 

Thanks so much for answering the question!

1 more question if possible - it asks me to plot each of the solutions on the interval t = 0 to 2 pi.

I did these things, however it says it only expected the range variable t in the expression but found names b1 and phase.

Here are the commands I have entered: 

m := 2;
k := 9;
omega := sqrt(k/m);
c1 := 0;
lambda := b1/(2*m);
gamma1 := sqrt(4*m*k-b1^2)/(2*m);
c2 := (-3+lambda*c1)/gamma1;
A := sqrt(c1^2+c2^2);
phase := arctan(c2/c1);
r1 := -b3/(2*m) + sqrt((b3/m)^2-4*omega^2)/2;
r2 := -b3/(2*m) - sqrt((b3/m)^2-4*omega^2)/2;
R := -b2/(2*m);

However, my c1 is zero because of the initial condition. This sets the phase as nonexistant.

The commands I entered to find the graphs were:

TheQuasiPeriod := (8*pi)/(sqrt(72-b1^2)) ;
b3QP := c1*exp(-abs(r1)*t)+c2*exp(-abs(r2)*t);
b2QP := (c1+c2*t)*exp(R*t);
b1QP := (A*exp(-lambda*t)*sin(gamma1*t+phase));

From there I entered in:

plot_b1:= plot(b1QP,t = 0..2*Pi):%;

plot_b2:= plot(b3QP,t = 0..2*Pi):% ;

plot_b3:= plot(b2QP,t = 0..2*Pi):% ;

However, its giving me the message 

Warning, expecting only range variable t in expression 12*(1/(72-b1^2))^(1/2)*exp(-1/4*b1*t)*sin(1/4*(72-b1^2)^(1/2)*t+phase) to be plotted but found names [b1, phase]

Could I get any help on this? It would be extremely appreciated as I am about to pass out dead from exhaustion. 

Thanks