Three identical masses are coupled together by four identical springs. The position of the left-most mass is xX1, the position of the next mass is x2 and the final mass is located at position x3 , as shown in the diagram below. k k ПО0 m X1 X2 X3 Using Newton's second law, we find the following equations govern the motion of these three masses. dx = -kx| – k(x1 – x2) di = -k(x2 – x¡) – k(x2 – x3) di? = -k(x3 – x2) – kx3 di? The natural modes of this system occurs for the following combinations of coordinates: Xa = X1 – X3 with angular frequency w, X, = x1 + v/2x2 + x3 with angular frequency », Xe = X1 = /2x2 + x3 with angular frequency w, . Given this, we can identify the natural frequencies by comparing our equation to the template simple harmonic oscillator equation: %3D di If m = 1.2kg and k = 885N/m, what is the largest natural frequency with which this system will oscillate? %3D %3D Answer: 1 The correct answer is: 50.2

Three identical masses are coupled together by four identical springs. The position of the left-most mass is xX1, the position of the next mass is x2 and the final mass is located at position x3 , as shown in the diagram below. k k ПО0 m X1 X2 X3 Using Newton's second law, we find the following equations govern the motion of these three masses. dx = -kx| – k(x1 – x2) di = -k(x2 – x¡) – k(x2 – x3) di? = -k(x3 – x2) – kx3 di? The natural modes of this system occurs for the following combinations of coordinates: Xa = X1 – X3 with angular frequency w, X, = x1 + v/2x2 + x3 with angular frequency », Xe = X1 = /2x2 + x3 with angular frequency w, . Given this, we can identify the natural frequencies by comparing our equation to the template simple harmonic oscillator equation: %3D di If m = 1.2kg and k = 885N/m, what is the largest natural frequency with which this system will oscillate? %3D %3D Answer: 1 The correct answer is: 50.2

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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Question

Three identical masses are coupled together by four identical springs. The position of the left-most mass is xX1, the position of
the next mass is x2 and the final mass is located at position x3 , as shown in the diagram below.
k
k
ПО0
m
X1
X2
X3
Using Newton's second law, we find the following equations govern the motion of these three masses.
dx
= -kx| – k(x1 – x2)
di
= -k(x2 – x¡) – k(x2 – x3)
di?
= -k(x3 – x2) – kx3
di?
The natural modes of this system occurs for the following combinations of coordinates:
Xa = X1 – X3 with angular frequency w,
X, = x1 + v/2x2 + x3 with angular frequency »,
Xe = X1 = /2x2 + x3 with angular frequency w, .
Given this, we can identify the natural frequencies by comparing our equation to the template simple harmonic oscillator equation:
%3D
di
If m = 1.2kg and k = 885N/m, what is the largest natural frequency with which this system will oscillate?
%3D
%3D
Answer: 1
The correct answer is: 50.2

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