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

Report 1

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

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

Spring
$F_{k} = - k * y$

Dashpot
$F_{c} = - c * y^{'}$
Mass
$F_{m} = m * y^{″}$
Forcing Function
$F_{a p p l i e d} = r (t)$

Sum of Forces
$\sum F_{a p p l i e d} + F_{m} + F_{c} + F_{k} = 0$

Substitution
$0 = r (t) - m * y^{″} - c * y^{'} - k * y$

$r (t) = m * y^{″} + c * y^{'} + k * y$

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