SOLUTION

If the initial condition is assumed to be zero means that the system is initially relaxed at time t =0 and no energy is stored in any of the components.

Zero initial condition for a system:

• Any parameter or physical quantity of a system like temperature, voltage, energy, etc is most of the time not constant. It varies with the time.
• These can be represented as differential equations or state equations in the s – domain.
• If the system is linear and shift-invariant, then the principle of superposition can be used and the output can be determined as a linear combination of the output due to the initial state (initial conditions) and the output due to the input sequence.
• When all of the initial conditions of a system are equal to zero, the system is designated to be relaxed (at rest) and no energy is stored in any of its components.
• We use LTI systems in practice. That means the system should be LINEAR. Zero initial conditions ensure Linearity. That is why Initial Conditions are assumed to be Zero in the transfer function model.