The equation of motion for a vibrating system with viscous damping is $$\frac{{{d^2}x}}{{d{t^2}}} + \frac{c}{m} \times \frac{{dx}}{{dt}} + \frac{s}{m} \times x = 0,$$ if the roots of the equation are __________ then the system will be under damped.
A. Equal
B. Real
C. Complex conjugate
D. None of these
Answer: Option C
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If the roots are real---- over damping
If the roots are imaginary or complex conjugate------ under damping
If the roots are equal ----- critical damping
how to c plz explain it