How Do Initial Conditions Affect Oscillations in a 10 Mass-Spring System?

  • Thread starter Thread starter wavey_simon
  • Start date Start date
  • Tags Tags
    System
Click For Summary
SUMMARY

The discussion focuses on calculating the eigenvalues and eigenvectors of a 10 mass-spring system to determine the resulting oscillations based on initial displacement and velocity conditions. Key concepts include the dot product of normal nodes and the superposition of normal modes, which are essential for understanding wave propagation and standing waves. The conversation emphasizes the importance of these calculations in predicting the system's behavior under various initial conditions.

PREREQUISITES
  • Understanding of eigenvalues and eigenvectors in mechanical systems
  • Familiarity with mass-spring system dynamics
  • Knowledge of wave propagation and standing wave theory
  • Proficiency in linear algebra concepts, particularly vector operations
NEXT STEPS
  • Research the calculation methods for eigenvalues and eigenvectors in mechanical systems
  • Explore the principles of superposition in oscillatory systems
  • Study wave propagation and standing wave formation in mass-spring systems
  • Learn about normal modes and their significance in oscillatory motion
USEFUL FOR

Students and professionals in physics and engineering, particularly those focused on mechanical systems, oscillatory motion, and wave dynamics.

wavey_simon
Messages
2
Reaction score
0
Hello!

I've been calculating the eigenvalues and eigenvectors for a 10 mass-spring system. If you are given some initial displacement and velocity conditions, what are the resulting oscillations?

dot or vector product of normal nodes? superposition of normal modes? etc

thanks if anyone can help me out
 
Physics news on Phys.org
10? that's enough to notice wave *propagation*, as well as the standing-waves that correspond to the normal modes.
 
yeah but assuming you don't notice propagation. just need to know how you calculate the resulting oscillation

ty
 

Similar threads

Two-level Quantum System - initial state
  • · Replies 14 ·
Replies
14
Views
3K
Understanding solution to equations of motion of n coupled oscillators
  • · Replies 4 ·
Replies
4
Views
3K
Why does this method of solving a system of 2nd order differential equations not work?
  • · Replies 13 ·
Replies
13
Views
2K
Analysing the Normal Modes and Dynamics of a Cluster of Atoms
  • · Replies 1 ·
Replies
1
Views
2K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
3K
Small oscillations and a time dependent electric field
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Is the Earth-Sun system an oscillator? What is an oscillator?
  • · Replies 11 ·
Replies
11
Views
2K
A system of 3 masses attached by springs is oscillating
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Pair of interacting systems, driven coupled harmonic oscillators
  • · Replies 7 ·
Replies
7
Views
3K
Spring with oscillating support (Goldstein problem 11.2)
  • · Replies 7 ·
Replies
7
Views
3K