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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.

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
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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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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