Problem 5: A helical spring of negligible mass is required to support a mass of50 kg. The stiffness of the spring is 60 kN/m. The spring and the mass system isdisplaced vertically by 20 mm below the equilibrium position and then released.Find: 1. the frequency of natural vibration of the system; 2. the velocity andacceleration of the mass when it is 10 mm below the rest position. [Ans. 5.5 Hz;0.6 m/s; 11.95 m/s²]

Answered: Image /qna-images/answer/5e683178-87db-4490-9589-b5adfb8bb4c5.jpg

Answered: Problem 5: A helical spring of…

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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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.
Problem 7: A 2 kg mass is hung from the end of a helical spring and is set vibrating vertically. The mass makes 100 complete oscillations in 55 s. Determine the stiffness of the spring. Also calculate the maximum amplitude of vibration if the mass is not to leave the hook during its motion.
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
In the suspended system as in the figüre, a) Examine the motion of mass m under the initial conditions of (c. < 2Vkm) and x (0) = 0 v(0) = Vo only in the case of springs and damping box. b) Examine the forced vibration motion that will occur when F (t) = Fo cos pt forcing force is applied in the same system under the same conditions. F() m /3 K/3
calculate the damping factor
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2. The mass ? = 20 kg is suspended from an ideal spring of stiffness ? = 500 N/m. If the mass is set into motion at ? = 0 with the initial conditions ?0 = 45.5 mm and ?0 = −104 mm/s, calculate (a) the amplitude of the motion; and (b) the time when the mass stops for the first time. Assume that ? is measured from the equilibrium position of the mass.
assuming that mass = 2150 kg K = 80.98 N/mm C =21.19 N/mm.
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.
#4 vibrations, will upvote anyone who will answer. Thanks
An sdof system consists of mass 175 kg and a spring constant k 530 kn/m while testing the system a relative velocity of 0.3 m was observed on application of force of 450 n determine the damping ratio
A vehicle suspension with mass of a single degree damped vibrating system of 8 kg makes 30 free oscillations in 15 seconds when disturbed from itse quilibrium position. The amplitude of vibration reduces to 0.3 of its initialv alue after five oscillations. Calculate: Stiffness (k) of the spring, logarithmic decrement damping factor

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