Please add a clear step by step solution with explanation 4.12. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass sub-jected to a vibrating base. For some applications, such as an automotive suspension,the magnitude of the response is not the critical factor, but rather the net force towhich the mass is subjected.1. Determine an expression for the force to which the mass illustrated in Figure 4.18is subjected.2. Manipulate the expression for the force so that it is in the form off = -khMfcos(@t+o).Explain the interpretation of the term Mf, which is called the force transmissi-bility. Plot Mf as a function of w/@n for various damping ratios to make a plotsimilar to Figure 4.20.displacement transmissibilty2.521.510.50012@n= 0.2= 0.4=0.6=0.8= 1.045Fig. 4.20 Displacement transmissibility as a function of frequency ratio and damping ratio.

Given:To find:Expression for forcePlot Mf as a function of

Answered: 4.12. Figure 4.20 plots the magnitude…

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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Figure 4 (a) shows a mechanical vibratory system. When 2 lb of force (step input) is appliedto the system, the mass oscillates, as shown in Figure 4(b). Determine m, b, and k of thesystem from this response curve. The displacement x is measured from the equilibriumposition
The nat. period of an undamped system is 3 s, but with a damping force that is proportional to the velcoity, the period becomes 5 s. Find the differential equation of motion of the system and its solution.
(a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its equilibrium position and allowed to vibrate. Show that the motion is simple harmonic. (b) A vertical helical spring having a stiffness of 1540 N/m is clamped at its upper end and carries a mass of 20 kg attached to the lower end. The mass is displaced vertically through a distance of 120 mm and released. Find : 1. Frequency of oscillation ; 2. Maximum velocity reached ; 3. Maximum acceleration; and 4. Maximum value of the inertia force on the mass. (c) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dashpot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the…
Find the natural frequency for the following systems (Assume that the rod has negligible weight and the oscillations are very small).
Derive the expression for motion and determine the natural frequency of the system shown in the figure below. Neglect the mass of the rod.
1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.
Derive the differential equation characterizing the motion of an oscillation system subjectto viscous damping and no periodic external force. Assuming the solution to the equation,find the frequency of oscillation of the system.
A single-story building frame is subjected to a harmonic ground acceleration as shown in Figure 7. Assume that M =1,099 kg, A=0.32 m/s^2 , ω=1.6 r/s and K=10,060 N/m. Find the maximum amplitude of the steady state motion of the floor in millimetre (mm).
Two masses m1 and m2 each connected by two springs of stiffness k, are connected by a rigid massless horizontal rod of length l as shown in Fig. 5.22. (a) Derive the equations of motion of the system in terms of the vertical displacement of the C.G. of the system, x(t), and the rotation about the C.G. of the system, θ(t) (b) Find the natural frequencies of vibration of the system for m1=50 kg, m2=200 kg and k = 1000 N/m.
2. Explain the oscillatory motion of damped springs and shockbreakee in car along with the physical quantities contained therein
1. A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of the spring from its equilibrium length, assuming it is hung vertically and neglecting the spring mass. 2. The mass in (1.) is pulled downward by an additional 6 cm and held steady. Calculate the potential energy input corresponding to this additional displacement. 3. Calculate the period of oscillation of the mass/spring system once the object is released. 4. Write an expression for the vertical motion of the system, along the y (vertical) axis, in the form: ?(?) = ? cos(?t) (Use the appropriate values of A and ω in your expression). 5. Calculate the maximum speed of the oscillating object and its maximum kinetic energy. Do your results make sense based off what you got in 2? (I posted all 5 parts but could you answer only 4 and 5? Thank you!)
A particle of mass m attached to a rigid support by a support of constant k. At equilibrium, the spring hangs vertically. This mass-spring system is joined by another identical oscillator, whose spring is hung from the previous mass. Consider only the vertical movement. a) write the equations of motion of the coupled system b)Compute the normal mode frequencies for one-dimensional vertical oscillations and then show that the ratio of the two normal frequencies is √5+1/√5−1 c)Find the ratio of the amplitudes of the two masses in each separate mode. (You do not need to consider the force of gravity acting on the masses because it is independent of the displacements.)

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