QUESTION 2A vibrating system can be modeled with a mass weighs 20 kg and supported on springs anddashpots. The total stiffness of the springs is 2000 N/m and the damping constant is 10 N/m/s. Thesystem is initially at rest and a velocity of 10 m/s is imparted on the mass. Determine thedisplacement after 1 s.

The objective of the question is to determine the displacement of a vibrating system after 1 second…

Answered: QUESTION 2 A vibrating system can be…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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For the system shown below, the disc of mass M rolls without slip. Assume that the mass M = 11 kg, the damping constant C - 209 Ns/kg and the stiffnesses K, = 9,036 N/m, K2 = 4,855 N/m, the radius of the disc R = 0.4 m and the moment of inertia of the disc about its centre I = MR² What is the damping ratio of the free vibration of this system? www K2 K1 M *No Slip
You are to investigate the vibration properties of the shock absorber system of a 2000 kg car. The shock absorbers drop 10 cm when the car is lowered from the lift and stands on its wheels. In addition, the amplitude decreases by 50% with each oscillation. Assume that the weight of the car is distributed evenly over all wheels and use the above information to determine the values for the spring constant k and the damping coefficient b. What error does the calculation deliver if the natural frequency of the shock absorbers ω is approximated by that of the undamped system ω_0?
Assume that you are examining the characteristics of a suspension system of a 2000 kg automobile. The suspension "sags" 10 cm when the weight of the entire automobile is placed on it. In addition, the amplitude of the oscillation decreases by 50% during one complete oscillation. Estimate the values of k and for the spring and shock absorber system of each wheel. Assume each wheel supports 500 kg.
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s
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19. A weight of 25 N is suspended from a spring that has a stiffness of 1,000 N/m. The weight vibrates in the vertical direction under a constant damping force. When the weight is initially pulled downward a distance of 10 cm from its static equilibrium position and released, it comes to rest after exactly two complete cycles. Find the magnitude of the damping force.
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.
An undamped free vibration system consisting of mass m = 5 kg and stiffnessa spring of 400 N/m, is given an initial displacement of 0.02 m and is kicked with an initial velocity of 0.1 m/s.Determine the equation of motion for the system.
A 2-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.5 m and reaches a maximum speed of 2 m/s. What is the spring constant in N/m?
A machine of mass 112.7 kg is mounted on four parallel springs each of stiffness 3.2 x 105 N/m. When the machine operates at 58.0 Hz, the machine's steady state amplitude is measured as 0.5 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: 3.49
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my''(t) +by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 20 kg, b = 80 kg/sec, k = 260 kg/sec², y(0) = 0.3 m, and y'(0) = -0.3 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point? (c) Find the frequency of oscillation for the spring system of part (a). (d) The corresponding undamped system has a frequency of oscillation of approximately 0.574 cycles per second. What effect does the damping have on the frequency of oscillation? What other effects does it have on the solution? (a) y(t) = plz answer a-d
A 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.3 m and reaches a maximum speed of 5 m/s. What is the spring constant in N/m?

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