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d. Explain what an equilibrium position is and how you can find them from a graph of potential energy versus position. Determine if there are any equilibrium positions using your potential energy function. For each position determined, are they stable or unstable?

d. Explain what an equilibrium position is and how you can find them from a graph of potential energy versus position. Determine if there are any equilibrium positions using your potential energy function. For each position determined, are they stable or unstable?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. An engineer working at an industrial spring company designs a spring that obeys a force law F(x) = -c(x – xeq)³ where c is a positive constant and xeg is the equilibrium position of the spring. a. What are the units of the constant c? Explain. b. Let the equilibrium position Xeq potential energy as a function of position. = 0 and derive an expression for the system's c. Make a graph of the force F(x) function and the potential energy U(x) function. d. Explain what an equilibrium position is and how you can find them from a graph of potential energy versus position. Determine if there are any equilibrium positions using your potential energy function. For each position determined, are they stable or unstable? e. Suppose you know the total energy of a system. What other information can be obtained from analyzing a potential energy graph? Explain.
Transcribed Image Text:1. An engineer working at an industrial spring company designs a spring that obeys a force law F(x) = -c(x – xeq)³ where c is a positive constant and xeg is the equilibrium position of the spring. a. What are the units of the constant c? Explain. b. Let the equilibrium position Xeq potential energy as a function of position. = 0 and derive an expression for the system's c. Make a graph of the force F(x) function and the potential energy U(x) function. d. Explain what an equilibrium position is and how you can find them from a graph of potential energy versus position. Determine if there are any equilibrium positions using your potential energy function. For each position determined, are they stable or unstable? e. Suppose you know the total energy of a system. What other information can be obtained from analyzing a potential energy graph? Explain.
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