See different possiblities for the critically
damped oscillator by varying C1 and C2

x(t)=C1exp(-βt)+C2*texp(-βt)

C2_1 = NaN
β = 1 (slider from 0 to 6, step 0.2)
C1_1 = 1 (slider from -5 to 5, step 0.1)
C2 = -3.9 (slider from -5 to 0, step 0.1)
ω = 4.4 (slider from 0 to 8, step 0.2)
C1 = 3.8 (slider from 0 to 5, step 0.1)
term2(t) = ((C2 * t) * ℯ^(((-β) * t)))
term1(t) = (C1 * ℯ^(((-β) * t)))
v0: C2 - (β * C1)
displ(t) = If[0 < t < 8, term1(t) + term2(t)]
C21 = NaN