Question

In which of the following cases, overdamping occurs?

(a) Roots are real

(b) Roots are complex conjugate

(c) Roots are equal

(d) Independent of the equation

I had been asked this question during an internship interview.

I want to ask this question from Frequency of Free Damped Vibrations topic in portion Longitudinal and Transverse Vibrations of Machine Dynamics

Answer 1

The correct answer is (a) Roots are real

To explain I would say: If the roots k1 and k2 are real but negative the case is of overdamping or large damping and the mass moves slowly to the equilibrium position. This motion is known as aperiodic.