1. Two Coupled oscillators Three ideal, massless springs and two masses are attached to each other as shown in figure 1. The extreme on the left hand side and on the right hand side are attached to fix walls. Neglect the effect due to gravity and consider k₁, k2, k12, M1, M2 > 0. k₁ wwwwwww m₁ x1 K12 wwwwwwwwwwww m₂ x2 wwwwww k₂ Figure 1: System of three ideal, massless springs with two masses. k₁, k2, k12, M1, M2 > 0 (a) Prove that the system in figure 1 always has two well defined normal modes. (b) What is the angular frequency of the oscillation for each normal mode if m₁ = m₂ = m and k₁= k₂= k k12? (c) What are the two normal modes if m₁ = m₂ = m and k₁ = k₂ = k = k12? Is the Center of Mass a normal mode? (d) What are the answers to the last two questions if k₁= k2 = k12 = k, and m₁ = m₂ = m?

1. Two Coupled oscillators Three ideal, massless springs and two masses are attached to each other as shown in figure 1. The extreme on the left hand side and on the right hand side are attached to fix walls. Neglect the effect due to gravity and consider k₁, k2, k12, M1, M2 > 0. k₁ wwwwwww m₁ x1 K12 wwwwwwwwwwww m₂ x2 wwwwww k₂ Figure 1: System of three ideal, massless springs with two masses. k₁, k2, k12, M1, M2 > 0 (a) Prove that the system in figure 1 always has two well defined normal modes. (b) What is the angular frequency of the oscillation for each normal mode if m₁ = m₂ = m and k₁= k₂= k k12? (c) What are the two normal modes if m₁ = m₂ = m and k₁ = k₂ = k = k12? Is the Center of Mass a normal mode? (d) What are the answers to the last two questions if k₁= k2 = k12 = k, and m₁ = m₂ = m?

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.57P: Find the stable equilibrium position of the system described in Prob. 10.56 if m = 2.06 kg.

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