Q4: - Using Laplace transforms to Find the displacementequation of mass (5 kg) attached with three elastic springs(4, 6, 2.6) N/m respectively as shown in Figure if the systemvibrates from rest under critical damping.Userm.

LAPLACE TRANSFORM is an integral transform that transforms a real variable function (typically time)…

Answered: Q4: - Using Laplace transforms to Find…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Q4: - Using Laplace transforms to Find the displacement equation of mass (3 kg) attached with three elastic springs (1, 3, 2.25) N/m respectively as shown in Figure if the system vibrates from rest under critical damping. ell
ROTATION SYSTEM -ENERGY METHOD Q1-A mass m is connected to a spring of stiffness k through a string wrapping around a rigid- pulley of radius R and mass moment of inertia I. Derive the equation of motion for the system fig (1) by energy method , find Tn , time response of the system.
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.
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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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Example # 1 For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates, as shown in fig. determi from this response curve. The displacement x is measured from the equilibrium position m, b, k of the system 0.0095 ft 0.1 ft 4 5 (b)
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2. Duffing's equation is a model for a dynamic system that includes a damping term and a nonlinear stiffness term. It most notably describes dynamics of electrical systems, but it has a simple analog as a nonlinear vibrations problem. Derive the non-homogeneous Duffings equation below using Hamilton's Principle. Start from the definition of the kinetic energy of a unit mass, and the virtual work of the springs and damper. Note, the spring force terms are both derivable from an energy function. x+cx+kx+vx³ = F sin sin(at)

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Q4: - Using Laplace transforms to Find the displacement equation of mass (5 kg) attached with three elastic springs (4, 6, 2.6) N/m respectively as shown in Figure if the system vibrates from rest under critical damping. Use