Solving an ODE: Seeking Help on Mechanics Problem

  • Thread starter Thread starter Pyroadept
  • Start date Start date
  • Tags Tags
    Mechanics Ode
Click For Summary
To solve the ordinary differential equation (ODE) (dS/dx)^2 + mw^2x^2 = a, first rearrange it to (dS/dx)^2 = a - mw^2x^2. Taking the square root of both sides yields dS/dx = ±√(a - mw^2x^2). This results in two separable differential equations, one for the positive root and one for the negative root. The next steps involve integrating both equations to find the general solution for S in terms of x. Understanding the separation of variables is crucial for solving this type of ODE effectively.
Pyroadept
Messages
82
Reaction score
0

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!
 
Physics news on Phys.org
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 -).
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

How to Approach Solving a Nonlinear Second Order ODE with a Quadratic Term?
  • · Replies 4 ·
Replies
4
Views
1K
How do we solve the ODE for the initial value problem with Burger's equation?
  • · Replies 5 ·
Replies
5
Views
2K
Continue solutions of ODEs around the origin
  • · Replies 2 ·
Replies
2
Views
1K
Differential Equation ODE Solution help.
  • · Replies 3 ·
Replies
3
Views
1K
Partial fraction decomposition with Laplace transformation in ODE
  • · Replies 9 ·
Replies
9
Views
2K
Solving a second-order differential equation
  • · Replies 33 ·
2
Replies
33
Views
4K
Solving a first order ODE using the Adomian Decomposition method
  • · Replies 7 ·
Replies
7
Views
2K
Solving an ODE by the method of Integrating Factors
  • · Replies 5 ·
Replies
5
Views
2K
Fourier Transformation of ODE
  • · Replies 2 ·
Replies
2
Views
2K
Solving a second order ODE using reduction of order
  • · Replies 2 ·
Replies
2
Views
2K