2- A damped single degree of freedom mass-spring system has a mass m = 5 kg, a spring stiffness k = 3,125 N/m, and a damping coefficient c = 25 N. s/m. The mass is subjected to a harmonic force which has an amplitude F₁ = 20 N and frequency w₁ = 10 rad/s. The initial conditions are such that x0 = 2 cm and v₁ = x = 0 m/s. Determine the displacement, velocity, and acceleration of the mass after t = 1 s. Determine the magnification factor and phase angle.

A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator.  Find the damping ratio of the system  ζ . Find the transmissibility of the system,  Tf. Find the frequency ratio of the system, β.          Find the amplitude of the harmonic excitation force of the system,  Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X  in millimeters (mm).  Find the damped frequency of the system,  ωd  in rad/s. Find the force transmitted to the foundation,  FT  in Newton (N). Find the frequency of the harmonic…

answer question 2 and 3

Find the free-vibration response of a spring-mass system subject to Coulomb damping for the following initial conditions x(0) = 0.5 m, *(0) = 0. Data: m= 10kg, k = 200 N/m, µ = 0.5. Q1 . ...

Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping?  Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant.  Using c=5.0, what is the new period of oscillation.  What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.

Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5 meters. L 2L k twine ww Figure 1-a A Rotational viscous damping coefficient b B g Massless a) Write the linearized equation of motion of the system (Figure 1-a) for small angular displacement 0 (t). (Symbolic)

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Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.

Answer ASAP would be appreciated

Obtain X1(s)/F(s) and then determine the damping coefficient C of the mechanical system below. m2 =160.1 kg, k =953.7 N/m, k, =1,451.7 N/m, b, =148.0 N-s/m. X1(t) x2(t) k2 f2(t) m2 k, b2 massless plate Sonraki