What characterizes an unstable system after a perturbation?

• A. The output stays within a fixed range
• B. The deviation grows unboundedly and diverges exponentially
• C. The system immediately shuts down
• D. The output tends to zero regardless of input

Answer: (B)

An unstable system after a perturbation is characterized by the behavior where any deviation from a state of equilibrium grows unboundedly and diverges exponentially. This means that if the system is disturbed even slightly, the effects of that disturbance will amplify over time rather than settle back to a state of balance.

In technical terms, systems that are unstable typically have positive feedback mechanisms or insufficient control to counteract disturbances. As a result, if the system is pushed away from its equilibrium state, it fails to return and instead continues to escalate the deviation, leading to increasingly large outputs or responses.

For example, consider a simple electronic feedback amplifier. If the feedback loop has a gain greater than one, any small input signal will cause an output that increases more than the input, leading to an exponential increase instead of stabilization.

The other choices describe different behaviors associated with stable systems, shut-down mechanisms, or systems that approach a steady-state value (like zero), but they do not accurately represent the characteristics of an unstable system.