Exercise 1. A mass trailer M, attached to a wall by a spring and a damper with damping coefficient c, slides over a frictionless surface, as illustrated by the Fig. 16. A uniform rigid bar, attached to the trailer by a pin, may oscillate relative to the pivot point, O. Derive the system movement equations under the applied forces F(t) and M(t) indicated in the image. Then obtain the natural frequencies and vibrate modes of the structure, where in this case the free system should be considered not dampened. Suppose the mass has length L and mass m.

damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…

The natural frequency of a system is determined to be 15 Hz ignoring the effects of damping. Calculate the damped natural frequency of the system assuming a damping ratio of 0.7.

A vehicle weighing 5,000 lb is supported on four identical springs and four identical viscous dampers. The static deflection of the vehicle under its own weight is 10 in. Determine the damping required for each of the dampers so that the critical damping is achieved.