Solve the following question by hand and without the use of AI. Use detailed mathematic Expressions and do not use AI. Thank You. Use the equation of motion for the system shown in the figure in Homework 1 to find01(5)the transfer function H₁(s) =H₂(s) =Om (5)02(5)Om(s)and H3(s) = Om(s) Note the massT(s)moments of inertia of the load and the motor are J₁ and Jm, respectively. T(t) is the inputtorque, 0₁(t) and 02 (t) are the output angles.Om FlexibleFlexible01Flexibleshaft02shaftshaftJ1MotorK1K₂JmK3RigidBshaftT(t)

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Answered: Use the equation of motion for the…

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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Derive the set of differential equations for a three mass-four sprang system as shown in Figure below that describes their time motion. Write the three differential equations in matrix form as figure attachment.
Consider the following spring system. m, C3 Cy m₂ C₂ Write the stiffness matrix K Write the matrix M ¹K C₁ = 6, m₁ = 6, C₂ = 12, m₂ = 3 Find the eigenvalues and eigenvectors of M ¹K: Smaller eigenvalue = with eigenvector • Larger eigenvalue = with eigenvector C3 = 18, C₁=6 If this spring system oscillates without any external forces present, then the position of each mass satisfies the following general formula: X 8 u(t) = (a₁ cos( t) + b₁ sin(t)) + (a2 cos (t) + b2 sin(t)) If the system begins oscillation with initial position u(0) = [] | and initial velocity (0) = [] then the position of the masses at time t is given by u₁(t): u₂(t):
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6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
= = Problem #2 - Modeling, Mass-Spring System Two masses are connected by springs in series as shown in Figure 1 below where k₁ 20 N/m, k₂ = 10 N/m, m₁ 10 kg, and m₂ = 5 kg. Solve the system of ODEs in matrix form using the determinant to obtain the characteristic equation (it will make sense to substitute > for w² when you get to your characteristic equation). Determine the eigenvalues (frequencies) and eigenvectors (modes) of oscillation. Assume that no damping is present and that the masses slide without friction. On your diagram, sketch the modes of oscillation (think of how the masses could oscillate with respect to each other). What determines which mode or combination of modes that the masses oscillate at? i.) ii.) iii.) iv.) v.) vi.) vii.) Sketch the system and include a free body diagram. Use a conservation equation to develop your differential equation model (you should end up with two ODEs to describe the motion of both masses). Write your system of ODEs in matrix form. Set…
All values equal to 1
Consider the following spring system. m. c2 = 10, c3 = , c4 = 2 C1 m2 = 2 Write the stiffness matrix K = Write the matrix MK Find the eigenvalues and eigenvectors of MK: • Smaller eigenvalue = with eigenvector • Larger eigenvalue = with eigenvector If this spring system oscillates without any external forces present, then the position of each mass satisfies the following general formula: u(t) = (a1 cos( t) + bị sin ( t) + (a2 cos( t) + bz sin( t) If the system begins oscillation with initial position u(0) = and initial velocity u'(0) = then the position of the masses at time t is given by u1(t) = uz(t) = Wir
A train mechanical system shown in Figure 1, consist of engine draw a car moving in one direction. The mass of the engine and the car will be represented by M1 and M2, respectively. The k is the stiffness coefficient of the spring held the two masses together and F represents the force applied by the engine, and the letter represents the coefficient of rolling friction. write the equations of motion in the form of: a- transfer function and b- state space. Where B1 = µM1g M1 M2 B2 = µM2 g В1 B2 Figure (1) a train mechanical system
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a. For the translational mechanical system shown in Figure (3). 1. Write the mathematical model in a format of matrices. 2. Find the transfer function G(s) = a₁ (s)/T (s) where a is the acceleration. t 45²² +16,5 245+628²-2-05+96 M₁ = 8 kg 6 N-s/m f(t) 1 N/m 0000 4 N-s/m -x₂(1) M₂-3kg Frictionless 0000 15 N/m Frictionless Figure (3) Translational mechanical system
Consider the following rotational mechanical system, a. Apply the "by inspection" method in Laplace domain to write the system of equations that represents the dynamics of the system b. Solve for the output variable q1(s). Use Cramer's rule or the substitution method to solve for the output variable q1(s). c. Give the transfer function G(s) = 91(s)/T(s) 0₁ (1) T(1) J1 82(1) oför J2 oooo K₁ K2 oooo D
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