mechanical vibration A mechanical system is governed by the two equations below. What are 1. the...
Please derive the equations and draw simulink model. For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main mass is eliminated? (b) What are the natural frequencies of the system? (c) Adding a damper to the absorber such that the absorber has a damping ratio of 0.5, how much would the main mass vibrate now? What if the excitation frequency...
1. For the mechanical system shown, A. Obtain the differential equations and set them in the matrix form. 2m B. find the natural frequencies and related amplitude ratios as functions of m and k. C. For m 4 Kg, k= 100 N/m, x,(0) 1, X2(0) 1, 1 (0) 0, *2(0) 0, find x (t) and x2 (t) in normal and general vibrations E WW 1. For the mechanical system shown, A. Obtain the differential equations and set them in the...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
QUESTION 10 Q8 (a): shock absorber for a car is to be designed. The system can be considered as simple SDOP system with a mass of m kg as shown in figure (below) and its damped free vibration response is shown beside that. The damped period of vibration is to be Td sec. n u It is observed that the amplitude reduced to,% of initial value after 2 oscillations. x(o) 2 For the above question, determine the damped natural frequencies...
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
arthe. ndr Problem 1: ur A free vibration of the mechanical system shown in the figure (a) indicates that the amplitude of vibration decreases to 25% of the value at t = to after four consecutive cycles of motion, as the figure (b) shows. Determine the viscous-friction coefficient b of the system if m = 1 kg and k= 500 N/m. x0.25 b K vad /s (a)
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
2. Assuming for a 2-DOF system the following eq uations of motion, andg so kip, g 386.4 in/s, k1 100 kip/in, Pi(t) 10 kip. P2(t) a. The two natural frequencies of the system. (25%) b. The two eigenvectors normalized with respect to mass and the 10 kip, determine the following: corresponding checks. (25%) c. Assuming a modal damping ratio ξ equal to 0.02, express numerically (as b, and N10) the uncoupled two equations of motion as shown below assuming classical...