Show all steps and solutions, vibrations For electromechanically system represented by the following mathematical Model4.6 × 10−1 + 4.93 × 10¯7x+ 0.380x = 0Determine(a) the response of the system if it has an initial velocity of 30.displacement of xo = 0 m.m-. mm and an initialsec(b) What is the value of the displacement at t = 1μs ?.

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Answered: For electromechanically system…

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 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)
For the system shown in Figure 2, u (t) and y (t) denote the absolute displacements of Building A and Building B, respectively. The two buildings are connected using a linear viscous damper with damping coefficient c. Due to construction activity, the floor mass of Building B was estimated that vibrates with harmonic displacement that is described by the following function: y(t) = y,cos (wt). k/2 Building A H k/2 M(t) C 73(1) Building B Equivalent (Building A) 00000000 Figure 2: Single-degree-of-freedom system in Problem 2. 111 uft) Please compute the following related to Building A: (a) Derive the equation of motion of the mass m. (b) Find the expression of the amplitude of the steady-state displacement of the mass m. (1) (Building B)
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1) For the mass-damper system at right, the model in terms of velocity is mv + cv = f. The time constant of this first order system is t = m/c. For this system, a larger value of the damping constant c causes the time constant to decrease - which is counterintuitive. It seems that a small amount of damping should correspond to a system with a fast response. How can you reconcile this? m CA
a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a. The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. The equations of motion of the system are given below. J₁ä + (mgL + kĽ² ) 8₁ - kľ² 0₁₂ = 0 J₁₂+(mgL+kĽ²)₂-kĽ² 0₁ = 0 i) Calculate the natural frequencies. ii) Draw the mode shapes. m Figure Q1a. b) In the above system discuss the implications of the following changes in coupling stiffness. i) k is reduced considerably to 0.1 N/m. ii) k is increased considerably to 1x105 N/m. c) Draw a schematic of modal test arrangement of a beam using instrumented impact hammer. d) Why is it necessary to measure force in a modal test?
Consider that the free response of the mechanical system is given by y(t) = 5e-at cos(2лƒ) (Eq. 1) whose plot is illustrated in Figure 3: Yh(t) 5 0 0,15 0,25 Arca 0,10 0,20 0,05 0,30 {[s] Figure 3 - Response of the mechanical system as described by Eq. 1. DETERMINE the frequency of damped oscillations of the system in Hertz and rad/s. Considering the damping factor as = 0.075, CALCULATE the system's natural (undamped) frequency. CALCULATE the stiffness of the system if its mass is 25 kg.

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