A certain armature controlled dc motor has the characteristic equation LaIs2 (RaI cLa)s cRa KbKT 0 Using the following parameter values Kh KT 0 1 N m A Ra 0 6 I 6 x 10 5 kg m2 Ln 4 x 10 3 H Obtain the expressions for the damping ratio and un damped natural frequency con in terms of the damping c Assuming that 1, obtain the expression for the time constant

Question: A certain armature-controlled dc motor has the characteristic equation LaIs2 + (RaI + cLa)s + cRa + KbKT = 0 Using the following parameter values:

A certain armature-controlled dc motor has the characteristic equation
LaIs2 + (RaI + cLa)s + cRa + KbKT = 0
Using the following parameter values:
Kh = KT = 0.1 N- m/A
Ra = 0.6 Ω
I = 6 x 10-5 kg-m2
Ln = 4 x 10-3 H
Obtain the expressions for the damping ratio ζ and un damped natural frequency con in terms of the damping c. Assuming that ζ < 1, obtain the expression for the time constant.

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