Complex Solutions to Oscillations

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SUMMARY

The discussion centers on solving oscillation equations, specifically focusing on the manipulation of first-order terms in differential equations. The user attempted to differentiate a given equation and substitute a trial solution, z(t) = e-iΩt, into another equation but encountered difficulties with the resulting first-order terms. Participants emphasized the importance of providing detailed attempts to facilitate accurate guidance and troubleshooting. The conversation highlights the iterative nature of solving complex mathematical problems and the necessity of clear communication in collaborative learning.

PREREQUISITES
  • Understanding of differential equations and their applications
  • Familiarity with complex functions, specifically exponential functions
  • Knowledge of oscillation theory and related mathematical models
  • Experience with trial solutions in solving differential equations
NEXT STEPS
  • Study the method of undetermined coefficients for solving differential equations
  • Learn about the application of trial solutions in oscillatory systems
  • Explore the concept of first-order differential equations and their solutions
  • Research techniques for manipulating and rearranging differential equations
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are dealing with oscillation problems and differential equations. This discussion is particularly beneficial for those seeking to improve their problem-solving skills in complex mathematical contexts.

WWCY
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Homework Statement


Screen Shot 2017-09-10 at 12.23.03 AM.png
Screen Shot 2017-09-10 at 12.22.55 AM.png


Homework Equations

The Attempt at a Solution


I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z.

I then tried using a trial solution provided: z(t) = e-iΩt and differentiating it according to what I derived above, before again, trying to rearrange them such that they would fit equation 2 had I subbed the trial solution into 2. I got stuck in both situations.

Any pointers and direction would be greatly appreciated
 
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Please show us your actual attempt instead of vaguely describing it. If you do not show us what you got, we can only guess where you went wrong.
 
WWCY said:
i got stuck with 2 first order terms z'
So reuse eqn 3.
 
haruspex said:
So reuse eqn 3.

I gave it a shot, does this look right?

21584608_10212603397174305_1475893820_n.jpg


If this is unreadable I'll upload an image of better quality later as I am on public transport right now, apologies!

Orodruin said:
Please show us your actual attempt instead of vaguely describing it. If you do not show us what you got, we can only guess where you went wrong.

I made a ridiculous error in my previous solution, i'll do up another one using the same line of reasoning and upload it to see where I went wrong.

Thank you both for the help.
 

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