Struggling with Dynamics Concepts?

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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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