
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Transcribed Image Text:1. Consider two pendulums, 1 and 2, with the same string length L, but with
different bob masses m1 and m2. They are coupled by a spring of spring
constant k, which is attached to the bobs. Find their equations of motion, for
small oscillations, solve for the modes and find their frequencies and
configurations.
2. Consider the system of three masses and four springs shown in the figure below.
Find the frequencies of the three normal modes for longitudinal oscillations. What
happens to the modes and frequencies when k1=k2? K1-3k2?
k1
k2
k2
k1
m
m
m
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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
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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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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
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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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For the system illustrated below, find the natural frequency.
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