1. An undamped spring-mass system is shown below. (a) Starting from the equations of motion, find the natural frequencies of the system if m₁ = m, m₂ = 2m, k₁=k, and k₂ = 2k. (b) Find the natural frequencies and mode shapes (i.e. modal vectors) of the system if m₁ = m₂ = 1 kg, k₁ = 2000 N/m, and k₂ = 6000 N/m. (c) Given the properties in (b), determine the response of the system x₁(t) and x₂(t) if the initial conditions are x₁(0) = 0.2 m, ₁(0) = x2(0) = 0, and ₂(0) = 5 m/s. Base k₁ 5 00000 m₁ NO k₂ m₂ x₁(1) x₂ (1) Undamped 2 DOF spring-mass system.

1. An undamped spring-mass system is shown below. (a) Starting from the equations of motion, find the natural frequencies of the system if m₁ = m, m₂ = 2m, k₁=k, and k₂ = 2k. (b) Find the natural frequencies and mode shapes (i.e. modal vectors) of the system if m₁ = m₂ = 1 kg, k₁ = 2000 N/m, and k₂ = 6000 N/m. (c) Given the properties in (b), determine the response of the system x₁(t) and x₂(t) if the initial conditions are x₁(0) = 0.2 m, ₁(0) = x2(0) = 0, and ₂(0) = 5 m/s. Base k₁ 5 00000 m₁ NO k₂ m₂ x₁(1) x₂ (1) Undamped 2 DOF spring-mass system.

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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