The differential equation of Damped Harmonic Oscillator

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SUMMARY

The discussion centers on the differential equation of the Damped Harmonic Oscillator, specifically addressing the condition where the damping ratio (b^2/m) exceeds four times the spring constant (4*k). In such cases, classic methods yield solutions, while alternative approaches involving complex numbers are necessary otherwise. The conversation also touches on the derivation of the differential equation, linking it to Hooke's Law and experimental verification. A resource from MIT OpenCourseWare is provided for further exploration of the topic.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with Damped Harmonic Oscillator concepts
  • Knowledge of Hooke's Law
  • Basic physics principles related to oscillatory motion
NEXT STEPS
  • Study the derivation of the Damped Harmonic Oscillator differential equation
  • Explore solutions using complex numbers in differential equations
  • Review the application of Hooke's Law in oscillatory systems
  • Investigate experimental methods for verifying oscillatory motion
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Students and professionals in physics, engineers working with mechanical systems, and anyone interested in the mathematical modeling of oscillatory phenomena.

Gh. Soleimani
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If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?
 
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I'm not sure what you mean by proving it.

If you find a solution you can always insert it into the differential equation to see if its true in the same way that the integral of some function when differentiated will produce the same function.

If you mean how did the differential equation for a damped harmonic come to be defined that would be more physics related with assumptions for the force of the spring (Hooke's law ie force proportional to spring stretch) and the motion verified by experiment.
 

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