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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 ....
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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.
- Spring '08