University of Florida/Egm4313/s12.team11.gooding.R1.r12

Derive the equation of motion of the spring-mass-dashpot, with an applied force ${\displaystyle r(t)\!}$ on the ball.

${\displaystyle y=y_{k}+y_{c}+y_{m}+r(t)\!}$

Spring
${\displaystyle F_{k}=-k*y\!}$

Dashpot
${\displaystyle F_{c}=-c*y'\!}$
Mass
${\displaystyle F_{m}=m*y''\!}$
Forcing Function
${\displaystyle F_{applied}=r(t)\!}$

Sum of Forces
${\displaystyle \sum F_{applied}+F_{m}+F_{c}+F_{k}=0\!}$

Substitution
${\displaystyle 0=r(t)-m*y''-c*y'-k*y\!}$

${\displaystyle r(t)=m*y''+c*y'+k*y\!}$

Created By:Kyle Gooding 01:46, 29 January 2012 (UTC)