Question

The system y(t) = \(\frac{d x^2 (t)}{dt}\) 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 in quiz.

This interesting question is from Characterization and Nature of Systems in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Correct choice is (a) Stable with input x(t)

For explanation: Given that y (t) = \(\frac{d x^2 (t)}{dt}\)

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

∴ y(t) = 2 \(\frac{d x(t)}{dt}\), That is not bounded output

The bounded input does not produce bounded output hence system is stable with input x (t) only.