Find the natural frequencies and modal vectors of the system shown in the nextfigure with m₁ = m, m2 = 2m, k₁ = k, and k₂ = 2k where m = 20 kg and k =1000 N/m.Note that the equation of motions of the system can bewritten asm₁x₁ + (k₁ + k₂)x₁ - k2x2 = 0-m2x2 + k2x2 − k₂x₁ = 0k₁Basek2m1x₁(t)00000m2x2(1)

The given two-mass system has two natural frequencies, 7.07 rad/s and 10 rad/s, at which it will…

Answered: Find the natural frequencies and modal…

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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Please answer: How many degrees of freedom are in the system Write out the equations of morion in matrix form & Find the natural frequencies Given: k = 10 N/m; r = 0.5 m; I1 = 1.25 kg*m2 ; I2 = 1.2 kg*m2; m = 1 kg
Derive the set of differential equations for a three mass-four sprang system as shown in Figure below that describes their time motion. Write the three differential equations in matrix form as figure attachment.
4
ll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112
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A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where k, is the suspension stiffness, m, the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 22 kN/m, m₁ = 304.3 kg, k₂ = 82.2 kN/m, and m₂ = 36.1 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring m₂ k₂ Tire stiffness Figure Q2 Answer: Wheel mass
vibrations
The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. k₁ k₂ K3 K= - (K₁ + K₂) k₂ m₁ = 1, m₂ = 5; k₁ = 3, k₂ = 15, k3 = 15 k₂ - (K₂ + K3) Describe the mode of oscillation for w₂. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The two masses move linearly, staying a fixed distance apart. B. The two masses oscillate in the same direction, where the amplitude of m₁ is O C. The two masses oscillate in opposite directions, where the amplitude of m₁ is D. The two masses oscillate in the same direction with equal amplitudes. E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m2. times the amplitude of m₂.
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A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where ky is the suspension stiffness, my the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 24.4 kN/m, m₁ = 257.5 kg, k₂ = 83.2 kN/m, and m₂ = 28.8 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring k₂ Tire stiffness Figure Q2 Answer: m₂ Wheel mass
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