Q3: Draw the free-body diagram and derive the equationof motion (EOM) using:(1) Newton's 2nd law(2) Energy method for the systems.(3) Find the natural frequency.m4r1447x(t)k00000-Pulley, massmoment ofinertia Jo

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Answered: Q3: Draw the free-body diagram and…

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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1. Draw the free-body diagram of the systmes depicted below and derive the differential equation describing the equation of motion (EOM) for each system. X (a) m - 3 kg k = 10 N m k₁ = N 3 kg m = www k₂ = 2 N m z (t) (b) (c) 1 = 7 m m = = 2 kg
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
Pls see the question in the attcahed image and solve using either Newton’s method or Lagrange Energy method .
For the system below, the mass, m is attached to the end of a cantilever beam of length, l, elasticity, E, and moment of inertia, I. Derive the equation of motions and find the natural frequencies in two cases by lagrange energy method a) k1=k2=0 b) k1≠k2≠0
PROBLEM1: Determine the equation of motion of the following systems: 1080 al*k www 0.51 ghiv Vin & Mass Less, Rigid L J Figure 2-Problem 1-2 a3*m
See the attached image. Please provide the solution modeled as a differential equation. Include an equation of motion of the mass for both no damping force and a damping resistance equal to half the velocity (please notate and show how to identify the velocity) with detailed steps and explanation of the solution.
F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.
If the 100 kg (Figure B1) mass has a downward velocity of 0.5 m/s as it passes through its equilibrium position. Each of the two springs has a stiffness k=180 kN/m , calculate: a) the equivalent spring stiffness( b) the natural frequency of the system c) the magnitude of its maximum velocity d) the magnitude amax of its maximum acceleration 100 ke Figure B1 wiw ww-
system with m=20, c = 17 Suppose that the mass in a mass-spring-dashpot and k = 3 is set in motion with x(0) = 0 and x'(0) = 8. (a) Find the position function x(t) and show that its graph looks as indicated in the figure. (b) Find how far the mass moves to the right before starting back toward the origin. 3 5 160 (a) x(t) = 7 (Type an exact answer.) 160 7 300 (b) The mass moves 7.1344 units to the right before turning back. (Round to four decimal places as needed.) 0 10 20 30 40 50
Find equation of motion and natural frequency for the system shown in fig. by energy method. H.W2// For the system Fig below find 1-F.B.D 2-Eq.of motion 8wn 4-0 (5) m. Jo m
Q.2 For the system shown; a- Derive the equations of motion using Lagrange method (use the Lagrangian). b- Determine the natural frequencies. c- Find and plot the mode shapes. d- What is type of coupling? m₁ my. Jo
Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128

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Q3: Draw the free-body diagram and derive the equation of motion (EOM) using: (1) Newton's 2nd law (2) Energy method for the systems. (3) Find the natural frequency. m 4r 1447 x(t) k 00000 -Pulley, mass moment of inertia Jo