Linear algebra decoupled system, answer in high detail k1kk2m1 W m2 WTwo masses are connected via three springs to each other and to the wallat left and right. The equations of motion are-k1x1 – k(x1 – x2) = m1ë1-k2x2 – k(x2 – x1) = m2ä2Suppose the force constants of the left and right springs are ki = k2 = 2and that of the center spring is k = 1. Let the masses be m1 = m2 = 1. Thetwo masses are given initial displacements at t = 0 of ı = 1 and x2 = 0.The initial velocity of each mass at t = 0 is zero.Your job is to calculate expressions giving the position of each mass as afunction of time using the diagonalization method discussed in class.

Given: -k1x1-kx1-x2=m1x¨1 -k2x2-kx2-x1=m2x¨2

Answered: k2 k1 W m1 W m2W k X.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear algebra decoupled system, answer in high detail

k1
k
k2
m1 W m2 W
Two masses are connected via three springs to each other and to the wall
at left and right. The equations of motion are
-k1x1 – k(x1 – x2) = m1ë1
-k2x2 – k(x2 – x1) = m2ä2
Suppose the force constants of the left and right springs are ki = k2 = 2
and that of the center spring is k = 1. Let the masses be m1 = m2 = 1. The
two masses are given initial displacements at t = 0 of ı = 1 and x2 = 0.
The initial velocity of each mass at t = 0 is zero.
Your job is to calculate expressions giving the position of each mass as a
function of time using the diagonalization method discussed in class.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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