Section 3. 7 Mass Spring Systems (Damped)
The IVP for Damped Free Vibration mu'' + γu' + ku = 0, u(0) = u 0, u'(0) = v 0 has positive coefficients m, γ, and k so this a special class of second order linear IVPs. In each of the three possible solutions exponentials are raised to a negative power, hence the solution u(t) in all cases converges to zero as t →∞. Discriminant γ2 – 4km > 0 distinct real roots solution