Damped Harmonic Oscillator Equation: Sum of Solutions = Another Solution?

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SUMMARY

The discussion centers on the damped harmonic oscillator equation and the property that any linear combination of its solutions is also a solution. Participants clarify that demonstrating this involves understanding the linearity of the equation. The key takeaway is that if two functions are solutions to the damped harmonic oscillator, their linear combination will also satisfy the equation, confirming the principle of superposition in linear differential equations.

PREREQUISITES
  • Understanding of differential equations, specifically linear differential equations.
  • Familiarity with the damped harmonic oscillator model in physics.
  • Knowledge of the principle of superposition in linear systems.
  • Basic mathematical skills for manipulating equations and functions.
NEXT STEPS
  • Study the properties of linear differential equations in detail.
  • Explore the mathematical derivation of the damped harmonic oscillator equation.
  • Learn about the principle of superposition and its applications in physics.
  • Investigate examples of linear combinations of solutions in various contexts.
USEFUL FOR

Students and professionals in physics, particularly those studying mechanics and wave phenomena, as well as mathematicians focusing on differential equations and their applications.

ambellina
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Hello,

I am confused about how to show that any two solutions of the damped harmonic oscillator equation equal another solution.

Thanks!
 
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ambellina said:
Hello,

I am confused about how to show that any two solutions of the damped harmonic oscillator equation equal another solution.

Thanks!

Do you mean you want to shown that a linear combinations of solutions is also a solution?
 

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