Answer to Question #314373 in Mechanical Engineering for Rimuru Tempest

Question

3.2.1 Write the state-space form of equation using the state assignments

X = [Vx iL]^t , y = Vx.

3.2.2 Write the state-space form of equation (7) using the state assignments

X = [Vx V×]^t , y = Vx

3.2.3 Show that the transfer function of the circuit in Figure 4, could be written :

G2(s) = Vx/Vu = 1/ (LCs² + CRs +1)

3.2.4 Show that the transfer function G2(s) could also be written as :

G3(s) = w²n/(s² + 2 ζwns + w²n) where the natural frequency is given as wn = 1/√LC .

What is the expression for the damping factor ζ.

Answer 1

The answer to your question is provided in the image: