Consider three identical masses, each with mass m, which slide frictionlessly along a hoop with radius R in the absence of gravity. The three masses are con- nected by identical springs which curl around the hoop. When the system is in equilibrium the three masses are arranged as in the figure, with the springs being at their natural lengths. For the coordinates, let us choose the three angles o1, 2 and o which indicate the masses' displacements from their equilibrium positions in the clockwise direction. 3. R (a) Write down the system's Lagrangian. (b) Derive the system's equations of motion and show that these can be cast in the form 2 I1 = -Mo = -u %3D -1 -1 -1 2

Consider three identical masses, each with mass m, which slide frictionlessly along a hoop with radius R in the absence of gravity. The three masses are con- nected by identical springs which curl around the hoop. When the system is in equilibrium the three masses are arranged as in the figure, with the springs being at their natural lengths. For the coordinates, let us choose the three angles o1, 2 and o which indicate the masses' displacements from their equilibrium positions in the clockwise direction. 3. R (a) Write down the system's Lagrangian. (b) Derive the system's equations of motion and show that these can be cast in the form 2 I1 = -Mo = -u %3D -1 -1 -1 2

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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