Why Do mω²xa and 2kxa Both Act in Normal Modes Oscillations?

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SUMMARY

The discussion centers on the dynamics of normal mode oscillations, specifically addressing the forces represented by the terms mω²xa and 2kxa. The participant initially questions the necessity of both terms in the equations governing oscillatory motion but later acknowledges confusion and attributes the complexity to gravitational effects. The key takeaway is that both mω²xa and 2kxa are essential in accurately describing the behavior of oscillating systems under the influence of gravity.

PREREQUISITES
  • Understanding of normal mode oscillations
  • Familiarity with the concepts of mass (m), angular frequency (ω), and spring constant (k)
  • Basic knowledge of gravitational forces and their impact on oscillatory systems
  • Ability to interpret and manipulate relevant equations in classical mechanics
NEXT STEPS
  • Study the derivation of normal mode oscillations in coupled systems
  • Explore the role of gravitational forces in oscillatory motion
  • Learn about the mathematical representation of oscillations using differential equations
  • Investigate the impact of varying spring constants on oscillation behavior
USEFUL FOR

Students of physics, particularly those studying mechanics and oscillatory systems, as well as educators seeking to clarify concepts related to normal mode oscillations and gravitational effects.

LCSphysicist
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Homework Statement
All below
Relevant Equations
All below
1594179721591.png


I am not sure if i get this part of a book i am using:

1594179748679.png


Why are the mwo²xa acting too? Is not 2kxa enough?
 
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Ignore it, i made a confusion :P need to sleep.
 
LCSphysicist said:
Homework Statement:: All below
Relevant Equations:: All below

View attachment 266042

I am not sure if i get this part of a book i am using:

View attachment 266043

Why are the mwo²xa acting too? Is not 2kxa enough?
It is due to gravity.
 
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