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Given that: k = 6000 N/m, r= 0.15 m, M=20 kg and mass moment of inertia for the pulley is J=0.36 kg. m2. Assume that the initial displacement x(0) = 20 mm and initial velocity *(0) = 0 m/s Final answer: 4r k --Pulley, mass moment of inertia J XCt)=20 cos(258A Wn = 25.819 Hz M (36)x+ 4000x=0 x(t) X d) = D cos(26:819t-W). 0 = 20

Given that: k = 6000 N/m, r= 0.15 m, M=20 kg and mass moment of inertia for the pulley is J=0.36 kg. m2. Assume that the initial displacement x(0) = 20 mm and initial velocity *(0) = 0 m/s Final answer: 4r k --Pulley, mass moment of inertia J XCt)=20 cos(258A Wn = 25.819 Hz M (36)x+ 4000x=0 x(t) X d) = D cos(26:819t-W). 0 = 20

Elements Of Electromagnetics
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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Question

Write down, natural frequency, the equation of motion and the solution (in terms of initial conditions) for the systems below:

Given that: k = 6000 N/m, r= 0.15 m, M=20 kg and mass moment of inertia for the pulley is J=0.36 kg. m². Assume that the initial displacement x(0) = 20 mm and initial velocity *(0) = 0 m/s Final answer: 4r -Pulley, mass moment of inertia J X(t)=20 cos(258AE w= 251819 Hz te M (36)x"+ Ruoodx =0 x(t) X it) = D cos(26:8ıdt-V). O = 20
Transcribed Image Text:Given that: k = 6000 N/m, r= 0.15 m, M=20 kg and mass moment of inertia for the pulley is J=0.36 kg. m². Assume that the initial displacement x(0) = 20 mm and initial velocity *(0) = 0 m/s Final answer: 4r -Pulley, mass moment of inertia J X(t)=20 cos(258AE w= 251819 Hz te M (36)x"+ Ruoodx =0 x(t) X it) = D cos(26:8ıdt-V). O = 20
Expert Solution
Step 1: Approach

Using the Equilibrium method as:
let us deflect the system by a small angle θ and then calculating the displacement of mass M and of spring K as:

x=rθ          x·=rθ·x··=rθ··         x1=4rθ 

all these variables are shown in the figure as:

 

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