s suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.

III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.

A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1   b.0.7   c.0.9     d.0.8 2)Calculate the magnification factor (M) of the system.  a.0.86    b.1.25     c.0.312     D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters).  a.0.2     b.0.1     c.0.4     D.0.3

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

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 F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s

Mechanical Vibrations Question is image

A SDOF system with a mass 25 kg and stiffness 10 N/mm with damping 0.15 Ns/m is initially at rest. IF the inital velocity is 100 mm/sec. find the expression for subsequent displacement .Hence find displacement and velocity at t=2 secs

For a single degree of system mass is 20kg stiffness=6.25kN/m damping coefficient 20Ns/m.Initial displacement at t=0 is zero and initial velocity is 150m/s obtain the equation of motion and find the displacement at 2seconds

For the mass spring system shown in figure spring constant (k 1 kg/m), mass= 8 kg and damping constant (C= 6 kg/sec). The steady state for this system is %3D k-IKg/m M-8Kg C-6 Kg/ sec

Consider a system of a uniform disc of mass Md and radius r attached on a vertical uniform rectangular rod of mass M which is constrained to oscillate left and right at a pivot point O by a harmonic excition force F = F, sin 50t applied at the top extremity of the rod as shown in the Figure Q1. For M=10kg M, = 5kg, F, =75N,k=8kN/m, c=360NS/m, r=0.12m and L=1.2m.