How Do You Derive the Equation of Motion for an Inverted Pendulum with Springs?

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In summary, the question asks for an explanation of the term with the red box in the given image, as well as clarification on the meaning of kl/2 and the sin and cos parts in the equation of motion for an inverted pendulum connected to two equal springs.
  • #1
2slowtogofast
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Can someone explain how they got the term with the red box
I understand the kl/2 but not the sin and cos part

**Question** Consider the inverted pedulum connected to two equal springs both with constant k. Springs are undelfected when the mass is in the verticle position. If the rod is of length l and the spring are connected at l/2 find the equation of motion.

http://img442.imageshack.us/img442/4896/24111q.jpg
 
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  • #2
2slowtogofast said:
Can someone explain how they got the term with the red box
I understand the kl/2 but not the sin and cos part
http://img442.imageshack.us/img442/4896/24111q.jpg

If that picture represents the total problem as presented, then there is no solution, as no question is asked?
 
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  • #3
Sorry I was on my phone and forgot the question I edited my orginal post
 

FAQ: How Do You Derive the Equation of Motion for an Inverted Pendulum with Springs?

Why is my pendulum solution not working?

There could be a few reasons why your pendulum solution is not working. One possibility is that the pendulum is not properly balanced or aligned. Make sure the string or rod holding the pendulum is straight and the weight is evenly distributed.

How can I fix my pendulum solution?

If your pendulum solution is not working, try adjusting the length of the string or rod to change the period of the pendulum. You may also need to make sure the pivot point is secure and the pendulum is free from any obstructions.

What is the ideal length for a pendulum?

The ideal length for a pendulum depends on the desired period or swing time. The formula for calculating the ideal length is L = (g x T^2) / (4π^2), where L is the length, g is the acceleration due to gravity, and T is the desired period in seconds.

Can temperature affect the accuracy of a pendulum solution?

Yes, temperature can affect the accuracy of a pendulum solution. Changes in temperature can cause the length of the pendulum to expand or contract, which can alter the period and therefore affect the accuracy of the solution.

How can I make my pendulum solution more accurate?

To make your pendulum solution more accurate, you can try using a longer pendulum length, using a more precise measurement for the length, or reducing external factors that may affect the pendulum's swing, such as air resistance or temperature changes.

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