Problem 2: Consider the block diagram shown in the figure below. Determine the values of K and k such that the system has a damping ratioE = 0.7 and an undamped natural frequency Wn = 4 rad/s. Please, use the block diagram algebra and the second

Problem 2: Consider the block diagram shown in the figure below. Determine the values of K and k such that the system has a damping ratioE = 0.7 and an undamped natural frequency Wn = 4 rad/s. Please, use the block diagram algebra and the second

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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The figure shows a vibratory system with two degrees of freedom; the OA bar is rigid and homogeneous of mass m = 6 kg and length l = 2 m.Suppose that:c1 = 200 kN s/mc2 = 600 kN s/mk1 = 500 N/mk2 = 300 N/m a) Determine the equations of motion of the system. b) Determine the matrices associated with the vibratory system. c) Determine the natural frequencies.
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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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
For the system shown in Figure, find: a) The system equation of motion in terms of θ b) The system natural frequency, ωn c) The system damping factor, ξ d)The system natural damped frequency
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
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3 Problem Consider the following model of a mechanical system: The system has a mass m, a linear spring with stiffness k, and two identical dampers with damping constant b. The left wall generates an input motion xin (t) that causes the mass to undergo a displacement x(t) from its equilibrium position. The initial position and velocity are zero. • Find the ODE describing the motion of the system by drawing a free-body diagram and applying Newton's 2nd Law. Your answer should be in terms of the following variables: Xin Xin, X, X, x, b,k, m Show that the transfer function is G(s) = - X(s) Xin(s) = 2b m k s+ m k s²+ + m When taking the Laplace transform L[xin(t)] you may assume the initial (input) condition Xin(0) = 0.
Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses moveto the right direction;a.Construct the free body diagram and develop the equation of motion for each mass.b.Write the equation of motion for the system in matrix form such that it is completewith all parameter values.c.Estimate the natural frequencies of the system where the spring coefficient, k1 = k2= k3 = k4 = 127 N/m and the masses, m1 = m2 = m3 = 17 kg.d.Determine the mode shapes of the system. Assume x1=1 in modal vectorNote: No need to sketch the mode shape diagram
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needs complete detailing. take N=70 b=20 a) The figure shows an oscillatory system where the mass 'M' is required to remain stationary even if an oscillatory force "Fo cos ot" acts on this mass 'M’. This mass 'M’ is a part of a simple harmonic system of stiffness 'k' and also connected to mass 'm' by a spring of stiffness 's'. If all oscillations are along the x-axis, find the value of frequency 'o' with which the small mass 'm' should oscillate to keep the mass 'M' stationary? Consider the following numerical values for calculations: M=100 kg, Fo cos ot m k=5 N/m, m='B’ kg, s='N' N/m