A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A secondparticle of mass 2m is suspended from the first particle by a second identical spring. The restlengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in thevertical direction.b)c)3md)2ma)How many degrees of freedom does the system have?[Expect to use a line to answer this question.]нееееееееkWrite down the Lagrangian of the system. Write down the Euler-Lagrange equations.[Expect to use about half a page to answer this question.]Find the equilibrium position of the particles.[Expect to use a few lines to answer this question.]Determine the frequencies and amplitudes of the normal modes.[Expect to use about half a page to answer this question.]e) Repeat the calculation with the gravitational force turned off. How do the normal frequen-cies change?[Expect to use a few lines to answer this question.]

Given:To find:Equilibrium position

A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction.

A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle of mass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the vertical direction.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second
particle of mass 2m is suspended from the first particle by a second identical spring. The rest
lengths of both springs are lo. The particles can only move vertically. Gravity acts as usual in the
vertical direction.
b)
c)
3m
d)
2m
a)
How many degrees of freedom does the system have?
[Expect to use a line to answer this question.]
нееееееее
k
Write down the Lagrangian of the system. Write down the Euler-Lagrange equations.
[Expect to use about half a page to answer this question.]
Find the equilibrium position of the particles.
[Expect to use a few lines to answer this question.]
Determine the frequencies and amplitudes of the normal modes.
[Expect to use about half a page to answer this question.]
e) Repeat the calculation with the gravitational force turned off. How do the normal frequen-
cies change?
[Expect to use a few lines to answer this question.]

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