Repeated Poles on Imaginary Axis

Correct Answer

A — Unstable

Concept and Reasoning

The equation (s²+4)²=0 gives poles at s=±j2, each repeated twice. Simple imaginary-axis poles can give marginal stability, but repeated imaginary-axis poles produce terms that grow with time, so the system is unstable.

Calculation / Key Relation

Poles: +j2,+j2,−j2,−j2

Exam Takeaway

Imaginary-axis poles must be simple for marginal stability.

Common Mistake

Do not classify repeated jω poles as marginally stable.