Differential Equations Eigenvalue!!!

[g4gate]

Consider the double mass spring system shown in the figure below.

The positions and of the two masses are given by the system

Let

and . If the forcing imparts a force

on the first mass and a force

on the second and the masses start from rest (

) and at their equilibrium positions (

), find the resulting motion of the system.

Attempt:

First I found the eigen values which are 16 and 24. Then found the respective eigenvectors:

for lambda = -9 v1 = 1 1

for lambda = -25 v2 = -1 1

So,

After that I am stuck... Please help...

Many Thanks!!!

 

[Deleted member 4993]

Consider the double mass spring system shown in the figure below.

The positions and of the two masses are given by the system

Let

and . If the forcing imparts a force

on the first mass and a force

on the second and the masses start from rest (

) and at their equilibrium positions (

), find the resulting motion of the system.

Attempt:

First I found the eigen values which are 16 and 24. Then found the respective eigenvectors:

for lambda = -9 v1 = 1 1

for lambda = -25 v2 = -1 1

So,

After that I am stuck... Please help...

Many Thanks!!!

DUPLICATE POST:

http://www.mathhelpforum.com/math-help/ ... ystem.html

Your problem asks you to: find the resulting motion of the system

What is it that they are looking for? Please explain what do you understand by the term "resulting motion"?

 

[g4gate]

Your problem asks you to: find the resulting motion of the system

What is it that they are looking for? Please explain what do you understand by the term "resulting motion"?

I just have to find the solution x_1 and x_2

 

[Deleted member 4993]

The eigen values you found - how can those be used in your "stiffness matrix" of the original equation?

Using those eigenvalues - you would uncouple the DE - and the solution is simple then.