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f(t) = A_{1}*e^{s1t} + A_{2}*e^{s2t}  Over Damped  Roots of the characteristic equation are real and unique. 
f(t) B_{1}e^{at} cos ( w t ) + B_{2}e^{at } sin ( w t )  Under Damped  Roots of the characteristic equation are complex. 
f(t) = D_{1}te^{at} + D_{2}e^{at}  Critically Damped  Roots of the characteristic equation are equal and real. 
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