Linear Constant Coefficient Differential Equations Zero-Input and Zero-State responses

1. How do you find the zero input and zero-state response?
2. What do you mean by zero-state response?
3. How do you find the zero-input response from a transfer function?
4. What is the relationship among a system's input its impulse response and its zero-state response?

How do you find the zero input and zero-state response?

To find the zero input solution, take the Laplace Transform of the input with f(t)=0 and solve for X_zi(s). Note: since the initial condition was doubled, the zero input response was doubled.

What do you mean by zero-state response?

In electrical circuit theory, the zero state response (ZSR), is the behaviour or response of a circuit with initial state of zero. The ZSR results only from the external inputs or driving functions of the circuit and not from the initial state.

How do you find the zero-input response from a transfer function?

Key Concept: The Zero Input Response and the Transfer Function. Given the transfer function of a system: The zero input response is found by first finding the system differential equation (with the input equal to zero), and then applying initial conditions.

What is the relationship among a system's input its impulse response and its zero-state response?

The impulse response of a system, possibly described by an ODE, is the zero-state response to an input signal x(t)=δ(t).