Solving an ODE: Seeking Help on Mechanics Problem

In summary, to solve the ODE (dS/dx)^2 + mw^2x^2 = a, one should first rewrite it as (dS/dx)^2 = a - mw^2x and then take the square root of both sides, including +/- on the right side. This will result in two separable differential equations, one for the positive and one for the negative solution.
  • #1
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Homework Statement


A point in a mechanics problem where I have to solve the ODE (dS/dx)^2 + mw^2x^2 = a

where m,w^2 are constants


Homework Equations





The Attempt at a Solution



Hi everyone,
We haven't actually covered how to solve these in my ODEs class yet (obviously my mechanics lecturer doesn't know this!). Please could someone point me in the right direction as to how to start it?
Thanks for any help!
 
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  • #2
Write the equation as (dS/dx)2 = a - mw2x, and then take the square root of both sides. Don't forget to include +/- on the right side.

Now you have two separable differential equations (one for +, one for -).
 

FAQ: Solving an ODE: Seeking Help on Mechanics Problem

What is an ODE?

An ODE, or ordinary differential equation, is a mathematical equation that describes the relationship between an unknown function and its derivatives. It is commonly used to model physical systems and solve various problems in mechanics, physics, and engineering.

How do I solve an ODE?

Solving an ODE involves finding an expression that satisfies the equation for the given function. This can be done through various methods, such as separation of variables, substitution, or using specific techniques for different types of ODEs. It is important to have a good understanding of calculus and mathematical concepts in order to solve an ODE effectively.

What is the importance of solving ODEs in mechanics?

ODEs are used extensively in mechanics to model the behavior of physical systems. By solving ODEs, we can predict the motion and behavior of objects in motion, such as projectiles, pendulums, and planetary orbits. This allows us to understand and analyze complex systems and make predictions about their behavior.

What are some common challenges in solving ODEs?

Some common challenges in solving ODEs include identifying the type of ODE (such as first-order or second-order), choosing the appropriate method to solve it, and handling complex or nonlinear equations. Additionally, finding initial or boundary conditions can also be a challenge in some problems.

How can I seek help on solving ODEs for mechanics problems?

If you are struggling with solving an ODE for a mechanics problem, there are several resources you can turn to for help. These include consulting with your professor or classmates, seeking help from a tutor, or using online resources such as forums and tutorials. It is also important to practice and work through similar problems to improve your understanding and proficiency in solving ODEs.

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