Underdamped Solution x ( t ) Plotted Using Maple

First define the solution x ( t ) as a function of t :

> x := t -> exp(–5*t) * ( –4 * cos(12*t) + 3 * sin(12*t) ) ;

Now plot the solution as t varies from 0 to 1. Here the vibrations dampen quickly.

> plot( x(t), t = 0.0 .. 1.0, color = blue, thickness = 5, size = [560,400] ) ;