Introduction

The circuit of Fig. 1 is required to be modeled using a state - space

representation, where 2 states will be used, based on the number of the energy -

storing elements of the circuit, the capacitor and the inductor.

R=20

Vin(s)

L = 0.1 H

mit(s)

C=800 μF

T

Vc(s)

Figure 1: Series LCR circuit

The input signal to the circuit is the voltage Vin (t) and the output signal is the

voltage across the capacitor, Vc (t). The current flowing in the circuit is denoted

by i, (t)./n6. Response to an initial condition (unforced response): Given that the input

voltage, Vin (t), is zero, calculate analytically the capacitor voltage

response, Vc (t), to the following initial condition,

x₁ (0)= i₂(0) = 0

x₂ (0) = Vc (0) = 5Volts

noting that the response of the system to an initial condition is given by,

x(t) = $(t)x(0)