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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2. Find the equation(s) of motion of the following system. How many DOF does this system have? The displacement of the mass is measured from the position where the spring is unstreched. Is this system linear or nonlinear? Define the state variables and express the equation(s) of motion in state form. Gravity should be included and the Coulomb friction coefficient of the rough ground is u. F,(0 x,(t) Friction, u
1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂
S:51)
Please solve the following question. Note that the second picture is the solution of the question from the book, I just want to know the steps to reach it.
This question asks for matrix form and NOT state space, but I don't understand what the difference between the two are.
Forcing Function Spring Constant f(t) k Mass m Friction Constant b Mass Displacement y(t) 3. Consider the following spring-mass-damper mechanical system (it is placed sideways, so that you won't need to consider gravity). The input is given by f(t), and the output is y(t). Find an equation in time domain that defines the relationship between the input f(t) and the output y(t).
3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T₂(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. u₂ denote T₂. You should expect to get the following state space representation and 9= KR + 0₁ 0 LIR -1. 7/2 Ti(t) Jun 0:0⁰ 40² T₂(t) 03 Figure 3: System for problem 3 21 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the ristic equation AS the system? iii. What are the values of the…
please solve (d, e, f)
Solve the following without the use of AI. Show all steps. Thank You!
Please answer in typing format Please answer in typing format Please answer in typing format please
Please also draw the FBDs
The figure that is attached illustrates a system in which a force F is applied to a mass m2 that is connected to another mass m1 via a spring and a damper, and mass m1 is connected to a wall via a damper. The equations of motion that govern the time evolution of the mass displacements, y1(t)and y2(t), are given below. A) Define 4 state variables of the system (xi, i = 1,…,4) as phase variables, and define the control input u. Convert the two equations of motion above into four 1st-order ODEs that are functions of the state variables and the control input.(b) Write the four 1st -order ODEs from part (a) in state-space form,x = Ax+Bu.

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