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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?

What will be the nature of time response if the roots of the characteristic equation are located on the s-plane imaginary axis? Correct Answer No oscillations

Roots of characteristic equation are located on s-plane imaginary axis then system is Marginally stable system. Marginally stable system: A linear time invariant system is said to be critically or marginally stable if for a bounded input its output oscillates at constant frequency and Amplitude. Such oscillation of output is called undamped or sustained oscillations. For such a system,one or more pairs of non-repeated roots are located on the imaginary axis. Complex conjugate (non-multiple): oscillatory (sustained oscillations) Complex conjugate (multiple): unstable (growing oscillations).

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