A railroad bumper is designed as a spring in parallel with a viscous damper. What is the bumper's damping coefficient such that the system has a damping ratio of 1.25 when the bumper is engaged by a 20,000-kg railroad car and has a stiffness of 2 x 10^3 N/m? In a moment the railroad car travels on a speed of 20 m/s when it engages the bumper. What is the maximum deflection of the bumper? Another empty railroad car has a mass of only 4500 kg. What are the natural frequency and a damping ratio of a system with the when engaged by an empty railroad car?

Consider the mass (W = 5 lbs) attached to a spring (k = 1 lb/in) as shown. Assume a short impulsive force is applied to the %3D mass to give it an initial velocity of 20 in/s. For the ensuing motion after the impulse is over: (a) Draw the degree of freedom on an appropriate figure. (b) Determine the equation of motion. What type of motion is this? (c) Determine the natural frequency of the vibration. Determine the period of the vibration. (d) Determine the displacement of the mass as a function of time. Plot the displacement vs time (clearly show important values). What is the maximum displacement that the mass will reach?

A 40 kg fan has a rotation unbalance of magnitude of 0.01 kg.m. The fan is mounted on a beam which is specially treated to have a viscous damping. By the variation of the speed of the fan, the amplitude of the vibration varies too. What is the fan's steady state amplitude when it operates at 1000 r/min? Givens: E = 200 GPa, I = 1.3 x10-6 m, L = 1.2 m, damping ratio = 0.06 Select one: O 2 mm 13.6 mm O 3.65 mm O 9 mm TOSHIBA

An m-mass pendulum is connected to a spring with the spring constant k through the massless rope along I as in the picture. x, i k www point y =0 m The spring is then given a deviation of x, so it moves at a speed of x. Assume point y = 0 is parallel to the spring, so that the potential energy of the pendulum negative value. If the pendulum has a deviation of 0, specify: The system motion equation uses the Euler-Lagrange equation.