Struggling with Dynamics Concepts?

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The discussion focuses on understanding dynamics concepts, particularly solving an ordinary differential equation (ODE) involving position x(t). The user is advised to differentiate x(t) to find dx/dt and d2x/dt2, then substitute these into the ODE to check for a solution. The user expresses frustration with the complexity of differentiation, indicating that the process has become messy. They seek confirmation on whether their approach is correct. The conversation highlights the challenges of applying calculus in dynamics problems.
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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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