The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x, '(0) = x,'(0) = 0) in its equilibrium position (x, (0) = x2(0) = 0) with the given external forces F, (t) = 0 and F,(t) = 270 cos 4t acting on the masses m, and m2, respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. k2 m k3 www - (k + k2) k2 www K= k2 - (k2 + k3) m, = 1, m, = 2; k, = 1, k, = 6, ką = 2 Find the resulting motion of the system. X4 (t) = X2(t) = (Type exact answers, using radicals as needed.)

The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x, '(0) = x,'(0) = 0) in its equilibrium position (x, (0) = x2(0) = 0) with the given external forces F, (t) = 0 and F,(t) = 270 cos 4t acting on the masses m, and m2, respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. k2 m k3 www - (k + k2) k2 www K= k2 - (k2 + k3) m, = 1, m, = 2; k, = 1, k, = 6, ką = 2 Find the resulting motion of the system. X4 (t) = X2(t) = (Type exact answers, using radicals as needed.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x, '(0) = x2'(0) = 0) in its equilibrium position (x, (0) = x2(0) = 0) with
the given external forces F, (t) = 0 and F, (t) = 270 cos 4t acting on the masses m, and m,, respectively. Find the resulting motion of the system and describe it as a
%3D
superposition of oscillations at three different frequencies.
k2
mi ww m2
k3
- (k, + k2)
k2
K=
k2
- (k2 + k3)
m, = 1, m, = 2; k, = 1, k, = 6, k3 = 2
%3D
Find the resulting motion of the system.
X4 (t) =
X2(t)
(Type exact answers, using radicals as needed.)

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