Navigating Damped and Forced Harmonic Motion

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SUMMARY

This discussion focuses on the concepts of Damped Harmonic Motion (DHM) and Forced Harmonic Motion (FHM), particularly for students lacking advanced mathematics background. A key mathematical result discussed is the complex exponential identity, e^(ipt) = cos(pt) + isin(pt), which is crucial for understanding DHM derivations. Participants seek clear online resources that explain these topics concisely, emphasizing the need for accessible explanations that include mathematical derivations.

PREREQUISITES
  • Understanding of basic harmonic motion concepts
  • Familiarity with complex numbers and exponential functions
  • Knowledge of power series expansions
  • Basic calculus skills for derivations
NEXT STEPS
  • Research online resources for Damped Harmonic Motion and Forced Harmonic Motion
  • Study the derivation of the complex exponential identity e^(ipt) = cos(pt) + isin(pt)
  • Explore power series and their applications in physics
  • Learn about the applications of DHM and FHM in real-world systems
USEFUL FOR

This discussion is beneficial for college students studying physics, particularly those interested in harmonic motion, as well as educators seeking to provide clearer explanations of these concepts.

Saoist
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hi guys,

doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources about FHM and DHM, maths included, but which explains clearly and concisely?

one major problem i have is that I've never seen the result:

e^(ipt)=cos(pt)+isin(pt) before. saw this in the middle of the DHM derivation which we were shown for all of 30seconds, scribbled it down.does anyone have a good derivation for this please?
 
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Actually it's the definition of the complex exponential.

But to see that it makes sense, simple plug ipt into the power series of e^x, and look at what you get.
 
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