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What will be the nature of time response if the roots of the characteristic equation are located on the s-plane imaginary axis?

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What will be the nature of time response if the roots of the characteristic equation are located on the s-plane imaginary axis?

(a) Oscillations

(b) Damped oscillations

(c) No oscillations

(d) Under damped oscilaations

This question was posed to me during an internship interview.

Enquiry is from Time Response of Second Order Systems topic in chapter Time Response Analysis, Design Specifications and Performance Indices of Control Systems

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Correct answer is (c) No oscillations

The explanation: complex conjugate (non-multiple): oscillatory (sustained oscillations)

  Complex conjugate (multiple): unstable (growing oscillations).

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