Suppose the differential equation governing the velocity of the mass of a hydraulic actuator in a system is given by the following, which is slightly different than the previous problem: b 1 Üm + + I Cf 62 vm + Um = = 12 A Ps(t). Cf (a) Give the steady-state value of vm for a unit step input given by Ps(t) = So t<0 1 t≥0 (b) Suppose the system is underdamped. Sketch the unit step response, taking care to show the steady-state value. (c) What are its natural frequency wn and damping ratio (? (d) Find the value of cf, in terms of b and I, that results in critical damping (e) Derive an ODE for the following state equation in terms of x2 d 16-82-8A dt x2 = 0 4 x1 + 0

Elements Of Electromagnetics
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Suppose the differential equation governing the velocity of the mass of a hydraulic actuator
in a system is given by the following, which is slightly different than the previous problem:
b
62
A
-Ps(t).
Cf
Üm +
(1+1/)
Um + 12 m
So t<0
(a) Give the steady-state value of vm for a unit step input given by Ps(t) =
t≥0
{1
(b) Suppose the system is underdamped. Sketch the unit step response, taking care to show the
steady-state value.
(c) What are its natural frequency wn and damping ratio (?
(d) Find the value of cf, in terms of b and I, that results in critical damping
(e) Derive an ODE for the following state equation in terms of x2
d
1
1
#2-832+838
[
dt
=
0 4
0 1
Transcribed Image Text:Suppose the differential equation governing the velocity of the mass of a hydraulic actuator in a system is given by the following, which is slightly different than the previous problem: b 62 A -Ps(t). Cf Üm + (1+1/) Um + 12 m So t<0 (a) Give the steady-state value of vm for a unit step input given by Ps(t) = t≥0 {1 (b) Suppose the system is underdamped. Sketch the unit step response, taking care to show the steady-state value. (c) What are its natural frequency wn and damping ratio (? (d) Find the value of cf, in terms of b and I, that results in critical damping (e) Derive an ODE for the following state equation in terms of x2 d 1 1 #2-832+838 [ dt = 0 4 0 1
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