2. Express the equation of motion of the damped 2DOF system depicted below, where p, q, andr are the horizontal coordinates and u₁, u2, and u3 are the forcing functions. Represent yourequation of motion in form of the state space representation with the general form below.k₁Ρալ√ x =Ax + Buy = Cx + DurqԱՅԱշКАk3k2wwwwM3M2C4C3C₁M1миC2

Here's what I can tell you about the system:There are four gears in the system: Gear A, Gear B, Gear…

Answered: 2. Express the equation of motion of…

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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1) Obtain a state space model of the system. 2) Given m =1 kg, k = 1 N/m and b = 1 N.s/m is the system Controllable? 3) For what values of k,m,b the system is stable? Explain your answer?
Represent the translational mechanical system shown in state space, where x3(t) is the output.
What is the step response of the dynamic system pictured below?
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
The magnitude of the steady-state response of an under damper and unforced spring-mass is
(system dynamics and control) q2 is given in image q3) ?
1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.
The equation of motion of a certain mass-spring-damper system is 5x'' + cx' +10x = f(t). How large must the damping constant c be so that the maximum steady-state amplitude of x is no greater than 3, if the input is f(t) = 22sin(wt), for an arbitrary value of w?
The block diagram shown is representing the dynamic system. Obtain the transfer function C(s)/R(s)by the method of reduction of blocks.
A suspension system of Volvo articulated dump truck is to be modelled mathematically given the following data: keq = 10.5 MN/m, m = 30 tons, and c = 300 N-s/m. If the harmonic forcing function is 2000 cos 5t N with the initial displacement and velocity to be 0 and 30 m/s respectively, determine the steady state and total response of the system.
The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly. C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).

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