A system is represented by the following differential equations:dy+ 1.5 + 4y = x. Find the natural frequency of oscillation.dt2dt

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Answered: E. Find the natural frequency 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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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 to which the mass is subjected. 1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected. 2. Manipulate the expression for the force so that it is in the form of f =−khMfcos(ωt+φ). Explain the interpretation of the term Mf , which is called the force transmissi- bility. Plot Mf as a function of ω/ωn for various damping ratios to make a plot similar to Figure 4.20.
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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.)
4 Assume that there's no damping. Please indicate if the system exhibits resonance.
Derivation of oscillation formulas
5. Find the natural frequency of the following system. Ignore the mass of the pulleys. k k m Figure 5:
A simple harmonic motion is defined by the expression a = - 25 s. Determine its period and frequency.
2 - A particle is subjected simultaneously to two SHMS of the same frequency and in the same direction. If their amplitudes are 1.5 mm and 2.5 mm respectively and the phase of the second component relative to the first is 40°, find the amplitude of the resultant displacement and its phase relative to the first SHM.
Q2: For a system the equations of motion are as shown below, find frequencies and mode shapes. Т Ţ X₂(1) muqu k, = k m₁ = m k₂= nk m₂ = m k₁ = k
Find the Equation of motion thenatural Frequency ssheaege for system below Ki k2 X2 X3
c and d

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E. Find the natural frequency of oscillation.