Lecture 1:20b

# Lecture 1:20b - Physics 315, Spring 2012 Note clarifying...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 315, Spring 2012 Note clarifying plus and minus signs in the solution of the SHO 1/23/2012 As we've seen, the general solution to the simple harmonic oscillator equation 2 2 2 d dt [ Z [ ¡ can be written as ¢ £ cos A t [ Z I ¡ or equivalently as ¢ £ ¢ £ cos sin B t C t [ Z Z ¡ . Since the differential equation is second order, its general solution must have two undetermined constants. These two constants are A and I for the first solution, and B and C for the second solution. The purpose of this note is to correct previous errors I've made about the signs of A , B , C , and . I There is no reason mathematically why A could not be a negative number. However, we normally adopt the convention that A is restricted to positive values. This can be done without loss of generality. For, suppose that we have a solution in the form ¢ £ 1 1 cos , A t [ Z I ¡ where A is a negative number. If we wish, we can define the new quantities 2 1 A A ¤ and 2 1 ....
View Full Document

## This note was uploaded on 02/13/2012 for the course PHY 315 taught by Professor Staff during the Spring '08 term at University of Texas.

### Page1 / 2

Lecture 1:20b - Physics 315, Spring 2012 Note clarifying...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online