Question

In which of the following cases, underdamping occurs?

(a) Roots are real

(b) Roots are complex conjugate

(c) Roots are equal

(d) Independent of the equation

This question was posed to me in quiz.

My doubt stems from Frequency of Free Damped Vibrations topic in division Longitudinal and Transverse Vibrations of Machine Dynamics

Answer 1

Right answer is (b) Roots are complex conjugate

To elaborate: If the roots k1 and k2 are complex, the case is of underdamping or small damping and the mass moves slowly to the equilibrium position.