Suppose the differential equation governing the velocity of the mass of a hydraulic actuatorin a system is given by the following, which is slightly different than the previous problem:b62A-Ps(t).CfÜm +(1+1/)Um + 12 mSo 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 thesteady-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 x2d11#2-832+838[dt=0 40 1

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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 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

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

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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