Zero input initial energy storage

What is the zero-input response?

The zero-input response is what the system does with no input at all. The System Equation relates the outputs of a system to its inputs. In addition, the initial conditions must be given to uniquely specify a solution. Solving the system equation tells us the output for a given input.

What is the zero-state response?

The zero-state response is the output of the system with all initial conditions zero. If H is a linear system, its zero-input response is zero. The zero-input response, which is what the system does with no input at all, is due to initial conditions, such as energy stored in capacitors and inductors.

What is a zero-input response in a linear system?

The response of a linear system can be decomposed into zero-input response and zero-state response. The zero-input response is the system output when the input , and thus it is the result of internal system conditions (such as energy storage, initial conditions) alone. Understand the zero-input behavior provides interesting insight into a system.

What happens when there's no input to the system?

When there's no input to the system, the zero-input response occurs. This is due to initial conditions, such as energy stored in capacitors and inductors. The zero-input response tells us what the system does with no input at all.

Why does a system respond in a zero state system?

It happens because it is completely independent of the input. The system responds just because of the storage energy. The second term, zero state response, it is the convolution of input and impulse response of the system. So, you need to find the impulse response of EDO.

How do you know if a linear system has a zero input?

If H is a linear system, its zero-input response is zero. This means that if the input is zero, the output will also be zero. This is known as homogeneity, which states that if y = F(ax), then y = aF(x). If a = 0, then a zero input requires a zero output.