This preview shows page 1. Sign up to view the full content.
Unformatted text preview: + K.E. = 1 2 m 2 a 2 = 1 2 sa 2 The total energy of a spring/mass system is a constant. Energy is juggled between tension in the spring (potential) and kinetic energy in the mass. We will nd this storage and exchange of energy in all oscillating systems. Note: Could have just integrated x + 2 x = 0 (twice) with respect to time to show that energy would be conserved without nding a solution of x and x . 3. Phase Space Diagram Mechanical systems completely characterised by knowing two variables: position x and velocity (momentum) x (or p = m x ) They are independent because both must be specied as initial conditions to solve F m x . For SHO we have x = a cos( t + ) and x = a sin( t + ) For = 0 these are ellipses in x, x space, with t = 0 starting along the xaxis at ( a, 0)...
View
Full
Document
This note was uploaded on 07/10/2011 for the course PHY 293 taught by Professor Pierresavaria during the Fall '07 term at University of Toronto Toronto.
 Fall '07
 PierreSavaria
 Physics, mechanics, Statistical Mechanics

Click to edit the document details