Determine the steady state response of the system shown in Figure Consider k₁ =1000 N/m, k₂ = 1500 N/m, k3 = 1000 N/m, m₁ = 10 kg, m₂ = 15 kg, f₁=300 sin 50t N.k1m1x1m2X2k3Note that the equation of motions of the system can be written asm₁ä₁ + (k₁ + k₂)x₁ - k2x2 = f₁-= 0m2x2 + (k2 + k3)x2 − k2x₁ =

Answered: Determine the steady state response of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Derive a model for the mechanical system represented below. The input being the force F and the output the displacement x. Determine the time response, x(t) when F is an impulse force of 100 Newton. K-50 kg/s² M=10 kg B-60 kg/s F (Vol Ans: x(t) = 2.5(e¹ - es)
A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where k, is the suspension stiffness, m, the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 22 kN/m, m₁ = 304.3 kg, k₂ = 82.2 kN/m, and m₂ = 36.1 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring m₂ k₂ Tire stiffness Figure Q2 Answer: Wheel mass
A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where ky is the suspension stiffness, my the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 24.4 kN/m, m₁ = 257.5 kg, k₂ = 83.2 kN/m, and m₂ = 28.8 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring k₂ Tire stiffness Figure Q2 Answer: m₂ Wheel mass
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
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Q2: Find the steady- state response of the system in Fig. below for the following data: kı=1000N/m, k=500N/m, c=500N.s/m, m=10kg, r=5cm, Jo=1kg.m², Fo=50N and 0=20rad/s Pulley, mass moment of inertia Jo k2 Fo sin wt m x(1) k
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State the equation that mathematically represents the system. All in domain X(s) hint: there are 2 equations k₁ oooo m₁ B₁ X1 (1) B3 k₂ 0000 M2 B₂ x₂ (1) k3 0000
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ll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112

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