Overdamped Motion

If we select = 1 and three different d -values: 12, 45, 96 ( ) , r named rk becomes:

> rk:=(d,m,k)->simplify(sqrt(d+4*m*k)):

> r=[seq(rk(d,1,1),d=[12,45,96])];

> plt1:=d->plot(xo(1,rk(d,1,1),1,2,t),t=0..20):

> txt1:=d->textplot([4,xo(1,rk(d,1,1),1,2,4),convert(r = rk(d,1,1),string)]):

> pltod:=display(seq({plt1(d),txt1(d)},d=[12,45,96]),labels=[`t`,`x(t)`],labelfont=[TIMES,BOLD,12]):%;

Figure 3 Overdamped motion, m = 1 kg, k = 1 , , r: damping constant

Figure 3 shows three typical graphs of the position function for the overdamped case. Figure 4 shows the animation of the motion with .

> mass_spring(1,4,1,0,5,2,0,14,0,60,scaling=constrained);

Figure 4 Animation of an overdamped motion of a mass-spring system with dashpot.
m = 1 kg, k = 1 , , r = 4