Question

The system y(t) = x^3(t) is ___________

(a) Stable with input x(t)

(b) Stable with output y(t)

(c) Stable with both input x(t) as well as output y(t)

(d) Not stable

This question was addressed to me by my college director while I was bunking the class.

I'm obligated to ask this question of Characterization and Nature of Systems topic in portion Laplace Transform and System Design of Signals and Systems

Answer 1

The correct choice is (c) Stable with both input x(t) as well as output y(t)

Easy explanation: Given that y (t) = x^3(t)

Let x (t) = u (t), that is bounded input

∴ y(t) = u^3(t) = u(t),  that is bounded output

The bounded input produces bounded output hence system is stable with both input x (t) as well as output y (t).