Register to reply

Spring-Mass System Matrix

by MysticalSwan
Tags: matrix, springmass
Share this thread:
MysticalSwan
#1
Mar22-12, 11:41 AM
P: 3
The differential equation that model an undamped system of 3 masses and 4 springs with external forces acting on each of the three masses is

m1x1''=-k1x1+k2(x2-x1)+u1(t)
m2x1''=k2(x1-x2)+k3(x3-x2)+u2(t)
m3x3''=k3(x2-x3)-k4x3+u3(t)

a)express the system using matrix notation x'=Kx+g(t) for the state vector x=(x1,x2,x3)T. Identify the matrix K and the input g(t).

b) Give conditions m1, m2, m3, k1, k2, k3, k4 under which K is a symmetric matrix.




I am pretty sure I have gotten the first part but I am having trouble even figuring out what the second part means. When I created my matrix K it seems like it is already a symmetric matrix. Any help would be great.
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
AlephZero
#2
Mar22-12, 05:12 PM
Engineering
Sci Advisor
HW Helper
Thanks
P: 7,177
I don't undestand part (b) either.

The equations you are given will be symmetric for any values of the m's and k's - so what was the question really asking you about


Register to reply

Related Discussions
Three spring two mass system, compression of the middle spring Introductory Physics Homework 3
Mass spring system where springs have mass Classical Physics 2
Spring Mass system where springs also have mass Introductory Physics Homework 1
What happens in acompletely reversing mass-spring system? (spring turns inside out) Introductory Physics Homework 2
Effect of mass and springs on the damping of mass spring system Classical Physics 5