Vibrations

1- A vibrating mass of 300 kg, mounted on a massless support by a spring of stiffness 40,000 N/m and a damper of unknown damping coefficient, is observed to vibrate with a 10-mm amplitude while the support vibration has a maximum amplitude of only 2.5 mm (at resonance). Calculate the damping constant and the amplitude of the force on the base.

8. Consider the system in Fig. 2, write the equation of motion,and calculate the response assuming (a) that the system is initially at rest, and (b) that the system has an initial displacement of 0.05 m.

In Problem 1.71, using the given data as reference, find the variation of the damping constant E when a. r is varied from 0.5 cm to 1.0 cm. b. h is varied from 0.05 cm to 0.10 cm. c. a is varied from 2 cm to 4 cm.

Sölve Problem 1.44 by assuming the wire diameters of springs I and 2 to be 1.0 in. and 0.5in. instead of 2.0 in. and 1.0 in., respectively.

Write a MATLAB code to plot the result of part a. Plot both f(x) and the result of part a. on the same figure. Find a power series expansion for f(x)=\frac{1}{1-x^{2}}

2. A lathe can be modeled as an electric motor mounted on a steel table. The table plus the motor have a mass of 50 kg. The rotating parts of the lathe have a mass of 5 kg at a distance 0.1 m from the center. The damping ratio of the system is measured to be = 0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the amplitude of the steady-state displacement of the

Problem 1 A falling weight deflectometer (see figure) is applied to a bridge at mid-span to initiate vibrations. After initial disturbance, the oscillations, which were measured using an accelerometer, were found to decay exponentially from an amplitude of 1.2g to 0.4g after five cycles of free vibration. Determine the damping ratio for the bridge girder. State your assumptions.

For the system shown in the figure a) determine the equation of motion of the equivalent linear system (at the mass "m" location) b) find the natural frequencies (ωn and ωd), c) the frequency ratio r. d) obtain the term X/δst using the graph (state the used points on the graph).

For the case when there is damping, c = 0, what is the phase angle if the displacement is of the form A* sin(@ot + p)?

1. Two springs each have spring constant k and equilibrium length/. They are both stretched a distance and attached to a mass m and two walls, as shown in figure below. At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length remains/). What is the resulting x(t)? Take the initial position to be x = 0.