D' Alembert's principle for critically damped condition

Q.  According to D' Alembert's principle, m (d2x/ dt2) + c (dx/dt) + Kx =0 is the differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is critically damped?
- Published on 11 Sep 15

a. x = (A + Bt) e– ωt
b. x = X e– ξωt (sin ωdt + Φ)
c. x = (A – Bt) e– ωt
d. x = X e– ξωt (cos ωdt + Φ)

ANSWER: x = (A + Bt) e– ωt

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