Struggling with Dynamics Concepts?

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SUMMARY

The discussion centers on solving ordinary differential equations (ODEs) using calculus concepts in dynamics. The user is advised to differentiate the function x(t) to find dx/dt and d2x/dt2, and then substitute these derivatives into the ODE to verify if the left-hand side matches the right-hand side. The approach emphasizes the importance of proper differentiation and substitution in confirming solutions to ODEs.

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  • Understanding of ordinary differential equations (ODEs)
  • Proficiency in calculus, specifically differentiation
  • Familiarity with functions and their derivatives
  • Experience with mathematical software like MathType for equation formatting
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  • Study the process of solving ordinary differential equations (ODEs) in detail
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Students in physics or engineering courses, particularly those studying dynamics and differential equations, as well as educators looking for effective teaching strategies in calculus and ODEs.

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Dynamics Trying to Understand??

Homework Statement




Homework Equations



I'm at a loss with this problem I was thinking integrating stuff but I really am having trouble?

The Attempt at a Solution

 

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You are given x(t) so just get dx/dt and d2x/dt2 and sub it into the ODE, if the LHS becomes the same as the right side, then it is a solution.

So start by finding dx/dt and d2x/dt2.
 


ok i started differentiating this and it got really messy but i put what i wrote down into mathtype and this is what i got for x-prime, am i in the right direction?
 

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