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 m, ^1 k₂ wwwwwww Ill₂ K3 www K= -(K₁ +K₂) k₂ m₁ = 1, m₂ = 5; k₁ =3, K₂ = 15, k3 = 15 k₂ -(K₂ + K3) Describe the mode of oscillation for @2. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The two masses move linearly, staying a fixed distance apart. OB. The two masses oscillate in the same direction, where the amplitude of m, is O C. The two masses oscillate in opposite directions, where the amplitude of m, is O D. The two masses oscillate in the same direction with equal amplitudes. O E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m₂. times the amplitude of m₂.

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 m, ^1 k₂ wwwwwww Ill₂ K3 www K= -(K₁ +K₂) k₂ m₁ = 1, m₂ = 5; k₁ =3, K₂ = 15, k3 = 15 k₂ -(K₂ + K3) Describe the mode of oscillation for @2. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The two masses move linearly, staying a fixed distance apart. OB. The two masses oscillate in the same direction, where the amplitude of m, is O C. The two masses oscillate in opposite directions, where the amplitude of m, is O D. The two masses oscillate in the same direction with equal amplitudes. O E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m₂. times the amplitude of m₂.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

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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