A 110 kg machine is mounted on an elastic foundation of stiffness 2×106 N/m. When operating at 150 rad/s, the machine is subjected to a harmonic force of magnitude 1500 N. The steady state amplitude of the machine is measured as 1.9 mm. Find • the frequency ratio the amplitude ratio or the magnification factor What is the damping ratio of the foundation?

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.

A structure that can be idealized as a SDOF system has a mass 100 kg, a stiffness of 40 kN/m and a damping ratio of 0.10. If it is subjected to a harmonic dynamic force given by p(t) = 500 sin(15 t) N, determine (a) the dynamic amplification under steady-state conditions; (b) the maximum velocity of the steady state vibration; and (c) the maximum amplitude if the forcing frequency was equal to the system frequency (a resonant condition).

Figure below shows a single degree of freedom system. The system has a moment of inertia I =37 kg.m² about point O, the stiffness and damping values are k =548 N/m and C =113 N.s/m, respectively. Considering a =1.6 m and b =0.7 m, find the damped natural frequency of the system in rad/s. a b C www