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

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SUMMARY

The discussion focuses on deriving the equation of motion for an inverted pendulum connected to two equal springs, each with a spring constant k. The key terms identified include kl/2, which represents the potential energy due to the spring's extension, and the trigonometric components involving sine and cosine, which are essential for analyzing the pendulum's angular displacement. The problem is framed with the pendulum's rod length l and spring attachment at l/2, emphasizing the need for clarity in the derivation process.

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  • Understanding of classical mechanics, specifically pendulum dynamics
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of trigonometric functions and their applications in physics
  • Basic proficiency in formulating differential equations
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  • Study the derivation of the equation of motion for a simple pendulum
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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 vertical 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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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?
 
Last edited by a moderator:
Sorry I was on my phone and forgot the question I edited my orginal post
 

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