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

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

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

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

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

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

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

Final Answer
$$r(t)=m*y''+c*y'+k*y\!$$

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