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The given D E is s^{\prime \prime}+b s^{\prime}+6 s=0Discriminant, D=b^{2}-4 a c=b^{2}-4 \times 1 \times 6=b^{2}-24We know, the soln will be overdamped if b^{2}>4 a c; critically demped if b^{2}=4 a c and underdamped if b^{2}<4 a cSo overdamped if b^{2}>24 ie (-\infty,-\sqrt{24}),(+\sqrt{24}, \infty)underdamped if b^{2}<24 ie (-\sqrt{24}, \sqrt{24}) \quad[\sqrt{24}=2 \sqrt{6}]critically damped if b^{2}=24 ic \{-2 \sqrt{6}, 2 \sqrt{6}\}[-2 \sqrt{6},-2 \sqrt{6}],[2 \sqrt{6}, 2 \sqrt{6}] ...