A precision grinding machine is supported on an isolator that has a stiffness of 1 MN/m and a viscous damping constant of 1 kN-s/m. The floor on which the machine is mounted is subjected to a harmonic disturbance due to the operation of an unbalanced engine in the vicinity of the grinding machine. Find the maximum acceptable displacement amplitude of the floor if the resulting amplitude of vibration of the grinding wheel is to be restricted to 106 m. Assume that the grinding machine and the wheel are a rigid body of weight 5000 N. (1) Grinding wheel Grinding machine

A machine of mass 203.5 kg is mounted on four parallel springs each of stiffness 1.6 x 105 N/m. When the machine operates at 47.2 Hz, the machine's steady state amplitude is measured as 1.0 mm. What is the magnitude of force transmitted to the foundations of the machine at this speed? The damping in the system is negligible. (Express answers to 3sf) Answer:

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).