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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.]

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter12: Coupled Oscillations
Section: Chapter Questions
Problem 12.22P
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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.]
Transcribed Image Text: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.]
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