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
Unformatted text preview: A c 1 sin = and A c 2 cos = . #8 Free Damped Motion We will assume that the damping force is given by a constant multiple of dt dx . The motions will be modeled by 2 2 2 2 = + + x dt dx dt x d where m = 2 , m k = 2 . Case I: 2 2The system is said to be overdamped . The solution is + =t e c e c e t x t t 2 2 2 2 2 1 ) ( . This equation represents a smooth an nonoscillatory motion. Case II: 2 2 =The system is said to be critically damped . The solution is ( 29 t c c e t x t 2 1 ) ( + =. Any slight decrease in the damping force would result in oscillatory motion. Case III: 2 2 <The system is said to be underdamped . The solution is ( 29 t c t c e t x t 2 2 2 2 2 1 sin cos ) (+=. #22...
View
Full
Document
 Fall '10
 PamelaSatterfield
 Differential Equations, Equations

Click to edit the document details