Learning to Solve Equations of Motion with fxns dx/Sqrt[E-U(x)]

In summary, the conversation revolved around the difficulty of integrating equations of motion involving functions of the type dx/Sqrt[E-U(x)]. The person was struggling because their lecturer only provided solutions using Mathematica, but they needed to be able to solve them on tests. The other person suggested trying the substitution u = 1 - e-ax, which would make the equation easier to solve.
  • #1
i'm learning how to integrate equations of motion but can't get very far solving anything because i can't figure out how to integrate fxns of the type dx/Sqrt[E-U(x)] . The only solutions my lecturer gives me to these questions are using mathematica but i need to do them in tests so i need to find a method. can anyone help me out?
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  • #2
Depends very much on the form of U(x).
  • #3
U(x) = A[1-e^(-ax)] is there a trick to solving this?
  • #4
It would seem obvious to me to try the substitution u= 1- e-ax.
Of course, you would then know that e-ax= 1- u.

1. What are equations of motion?

Equations of motion are mathematical representations of the relationships between an object's position, velocity, and acceleration over time. They are used to describe the motion of objects in a variety of scenarios, such as free fall or projectile motion.

2. Why is it important to learn how to solve equations of motion?

Solving equations of motion allows us to accurately predict and analyze the motion of objects in various situations. This is crucial for understanding and designing systems in fields such as physics, engineering, and mechanics.

3. What are fxns dx/Sqrt[E-U(x)] and how are they used in equations of motion?

fxns dx/Sqrt[E-U(x)] is a mathematical expression used to calculate the change in an object's position over time. It represents the relationship between the object's position, energy, and potential energy.

4. How can I effectively learn to solve equations of motion?

To effectively learn to solve equations of motion, it is important to have a strong understanding of basic mathematical concepts such as algebra and calculus. Practice and repetition are also key, and working through various examples and problems can help improve understanding and proficiency.

5. Are there any common mistakes to avoid when solving equations of motion?

Some common mistakes to avoid when solving equations of motion include not properly identifying and labeling the variables, not using the correct formulas or equations, and not paying attention to units and their conversions. It is also important to check your work and make sure the final answer makes sense in the context of the problem.

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