Figure 1 shows a system with two different masses with mass m, connected by springs withstiffness k. Given that k, = 60, k2= 10, k3= 0, m1 = 20, m2 = 2.x1(t)X2(t)k1k2k3WH m,m2Figure 1: Free vibration of undamped linear systems with two degrees of freedom.i. Sketch the free body diagram associated to the system shown in Fig. 1.ii. Derive the equation of motion of the system.iii. Find the characteristic equation of the system through matrix notation from theequation derived in (ii).iv.Find the natural frequencies (eigenvalues).Find the natural modes (eigenvectors).Given the initial conditions of the systems motion when t=0 is x1(t) = 0, x2(t) =1, *1(t) = 0, *2(t) = 0, find the free vibration respons es of m, and m2.What would happen when mass m, is excited by the force F(t) = F10 cos wt? You arerequired to modify the equation of motion obtained in (ii) and state the effect of forcedvibration to the system.V.vi.vii.

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Description: Figure 1 shows a system with two different masses with mass m, connected by springs withstiffness k. Given that k, = 60, k2= 10, k3= 0, m1 = 20, m2 = 2.x1(t)X2(t)k1k2k3WH m,m2Figure 1: Free vibration of undamped linear systems with two degrees of fr

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Answered: Figure 1 shows a system with two…

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Figure 1 shows a system with two different masses with mass m, connected by springs with stiffness k. Given that k, = 60, k2= 10, k3=0, m, = 20, m2 = 2. x, (t) X2(t) k1 k2 k3 ww m, m2

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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A body of mass 100 kKg is suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.
Question 1. A body of mass 100 kKg is suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.
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