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.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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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
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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