Solve Air Spring Equations for Walking System

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The discussion focuses on modeling a walking system that utilizes an air spring, with a specific energy equation provided for the air spring. The user seeks assistance in deriving the force equation from the energy equation to apply it within Newton's second law of motion. Clarification is requested regarding the term "king of walking system," which is identified as a typo for "kind of walking system." The relationship between force and potential energy is emphasized, with the formula F(x) = -dU/dx being noted as crucial for the calculations. Overall, the thread centers on the mathematical modeling of the air spring's behavior in a walking system context.
ajal
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Hi,

I am modeling some king of walking system, and I need to use air spring. The one that is conventionally used (I think so) has an energy equation like:

U(x) = K/2 * (1/x^2 - 1/x0^2)

I am trying do derive the "force" equation for this air spring so I can use if with Newton's second law equations of motion.

Would you please help me with this. Thanks.
 
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Please explain this "king of walking system". Is it a system that allows you to walk like a king or is it the king of all "walking systems" (whatever a walking system is)?
 
:)) typo:

king of --> kind of
 
Force is connected with potential energy with this formula:

F(x)=-dU/dx
 
Thanks! Helped!
 

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