Rayleigh's Method

For simple harmonic motion, when PE is maximum and KE is minimum and the other way around.
$P{E}_{\max }+K{E}_{\min }=P{E}_{\min }+K{E}_{\max }$
See OneNote for example of using Rayleigh’s method.

Conversation of energy

Isn’t this equation basically just conservation of energy???

General Strategy

We want to use the Rayleighs method to find some sort of maximum or minimum displacement

1. Write expressions for PE and KE
2. Find when PE and KE is maximum and minimum with respect to their independent variables (usually x or theta)
   1. The key to Rayleighs is setting |X_max| = A so that, X_max’=w_n*A
3. Find equivalent mass / spring constant (or both)
4. Equate using Rayleighs method
5. Solve for whatever you are looking for (equation or motion, natural frequency etc)