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

Report 1

R1.2

Problem Statement

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

Figures

Derivation

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)