Question

Zero initial condition for a system means ____ .

• A. Input reference signal is zero
• B. Zero stored energy
• C. The initial movement of moving parts
• D. System is at rest and no energy is stored in any of its components

Hint:

Zero Initial Conditions. Implies the system starts from a state of rest with no stored energy in its dynamic elements (e.g., zero initial inductor currents, capacitor voltages, displacements, velocities) just before the input is applied.

Answer 1

The Correct Option is D

When analyzing dynamic systems, particularly using techniques like Laplace transforms to find transfer functions or responses, the "zero initial condition" assumption is often made
This assumption simplifies the analysis by focusing on the system's response to the input signal itself, without influence from prior states
Zero initial condition means that before the input signal is applied (at \(t=0^-\) or \(t=0\)), the system is in a state of equilibrium or rest, and there is no energy stored in any of its energy-storing elements
- For electrical circuits, this means initial currents through inductors and initial voltages across capacitors are zero
- For mechanical systems, this means initial displacements and velocities are zero
Option (4) accurately describes this state: the system is at rest (zero initial velocities/currents) and has no stored energy (zero initial displacements/charges)
Option (2) is part of the condition but doesn't include the "at rest" aspect
Option (1) refers to the input signal, not the system's initial state
Option (3) describes an initial state, but not necessarily a zero initial condition