The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′(0)=x2′(0)=0)in its equilibrium position (x1'(0)=x2'(0)=0) with the given external forces F1(t)=0 and F2(t)=540 cos 4t acting on the masses m1and m2, respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3 m1=1, m2=2; k1=1, k2=2, k3=2 Find the resulting motion of the system. x1(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 (x1′(0)=x2′(0)=0)in its equilibrium position (x1'(0)=x2'(0)=0) with the given external forces F1(t)=0 and F2(t)=540 cos 4t acting on the masses m1and m2, respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3 m1=1, m2=2; k1=1, k2=2, k3=2 Find the resulting motion of the system. x1(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.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′(0)=x2′(0)=0)in its equilibrium position (x1'(0)=x2'(0)=0) with the given external forces F1(t)=0
and F2(t)=540 cos 4t acting on the masses m1and m2,
respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies.
and F2(t)=540 cos 4t acting on the masses m1and m2,
respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies.
|
m1
m2
k1
k2
k3
x1
x2
|
K=
|
m1=1, m2=2; k1=1, k2=2, k3=2
Find the resulting motion of the system.
|
x1(t)
|
=
|
|
|
x2(t)
|
=
|
(Type exact answers, using radicals as needed.)
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