A Y2 B Figure 11.19 Problem 11.24 11.24✶✶ Two equal masses m move on a frictionless horizontal table. They are held by three identical taut strings (each of length L, tension 7), as shown in Figure 11.19, so that their equilibrium position is a straight line between the anchors at A and B. The two masses move in the transverse (y) direction, but not in the longitudinal (x) direction. Write down the Lagrangian for small displacements, and find and describe the motion in the corresponding normal modes. [Hint: "Small" displacements have y₁ and y2 much less than L, which means that you can treat the tensions as constant. Therefore the PE of each string is just Td, where d is the amount by which its length has increased from equilibrium.]

A Y2 B Figure 11.19 Problem 11.24 11.24✶✶ Two equal masses m move on a frictionless horizontal table. They are held by three identical taut strings (each of length L, tension 7), as shown in Figure 11.19, so that their equilibrium position is a straight line between the anchors at A and B. The two masses move in the transverse (y) direction, but not in the longitudinal (x) direction. Write down the Lagrangian for small displacements, and find and describe the motion in the corresponding normal modes. [Hint: "Small" displacements have y₁ and y2 much less than L, which means that you can treat the tensions as constant. Therefore the PE of each string is just Td, where d is the amount by which its length has increased from equilibrium.]

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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