This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 4.9; Section 5.6 Free Mechanical Vibrations/Couple MassSpring System April 14, 2009 Free Mechanical Vibrations/Couple MassSpring System Todays Session A Summary of This Session: (1) Free Mechanical Vibration (no forcing term). (2) Coupled MassSpring systems (3) Our first exposure to systems of differential equations (4) Eigenvalues and Eigenvectors Free Mechanical Vibrations/Couple MassSpring System Free Mechanical Vibrations Free mechanical vibration=no forcing function, so f ( t ) = 0. We are dealing with my + by + ky = 0 where m = mass attached to a spring of stiffness k , subject to friction (or damping) proportional to speed with damping constant b . Four cases: (1) undamped free case; (2) underdamped case; (3) overdamped case; (4) critical damped case. Free Mechanical Vibrations/Couple MassSpring System Case 1: Undamped massspring system: b = 0. The equation is given by: my + ky = 0 or y + k m y = 0 Let 2 = k m . The quantity = radicalBig k m is called the angular frequency (measured in radians per second) Period: T = 2 (measured in seconds) Frequency: f = 1 T = 2 (measured in Hertz=1/seconds=# cycles per second) The solution is given by: y = C 1 cos t + C 2 sin t = A sin( t + )....
View
Full
Document
This note was uploaded on 10/06/2009 for the course MATH 254 taught by Professor Indik during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 INDIK
 Differential Equations, Equations

Click to edit the document details