Elements Of Electromagnetics

7th Edition

ISBN: 9780190698614

Author: Sadiku, Matthew N. O.

Publisher: Oxford University Press

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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.)

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For given mass (m=10kg) and two springs systems k1=30 N/m and k2= 20N/m. Find the following
1. Circular Frequency and natural frequency
2. If initial displacement is 50 mm and initial velocity is 0, what is max displacement and max velocity.
3

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Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released,
With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A.
p.s. This question was previously answered but because the solution images were unable to view I need to re-ask this question

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a coupled pendulum system is in vertical plane as shown.each rod of mass m and length l and can freely oscillate about point of suspensions.write equation of motion for both the rods and find frequencies of normal modes.find out ratios of amplitudes of the two oscillators for exciting normal modes

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Problem 1
A weight of 50 N is suspended from a spring of stiffness 4000 N/m and is subjected to
a harmonic force of amplitude 60 N and frequency 6 Hz. Find
(a) the extension of the spring due to the suspended weight,
(b) the static displacement of the spring due to the maximum applied force, and
(c) the amplitude of forced motion of the weight.

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A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal spring is attached to the glider, and the other end is attached to the end of the track. When released, the glider oscillates in SHM with frequency 4.15 Hz. Find the period of the motion.
Find the angular frequency of the motion. Find the force constant kk of the spring.
Find the magnitude of the force that the spring exerts on the glider when the spring is stretched by 0.0200 m.

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Question 3 Figure 3 shows a uniform beam is supported horizontally by two equal springs of the same stiffness. Derive the equation of the two frequencies of small oscillations in the vertical plane. Show that the two frequencies will be equal only if 3acb== c2abxG

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Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released,
With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A.

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A weight of 50 N is suspended from a spring of stiffness 4000 N/m and is subjected to a harmonic force of amplitude 60 N and frequency 6 Hz. Find the static displacement of the spring due to
the maximum applied force?

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For the system illustrated below, ﬁnd the natural frequency.

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Two masses of weight 300 N each are keyed to the opposite ends of a shaft. The shaft length is 70 cm. The shaft is 7 cm diameter for the first 30 cm of its length, 13 cm diameter for the next 20 cm, and 10 cm diameter for the remaining of its length. Find the frequency of free torsional vibrations of the system and the position of the node. The radius of gyration of the masses is 30 cm.

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A torsion pendulum is made using a steel wire of radius 0.25 and sphere of of diameter 11300kg/m^3.If the period of oscillation is 2second,find the the length of the wire

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