User:Egm4313.s12.team11.arrieta/Report 1

Problem Statement

 * Derive the equation of motion of a spring-dashpot system in parallel, with a mass and applied force $$ f(t)$$.



Kinematics:


 * $$ y=y_k=y_c \!$$         (1)


 * Since the spring and dashpot are placed parallel to each other, they will experience the same deformation when a force $$ f(t) $$ is applied on the system

Kinetics:


 * $$ f(t)-f_k-f_c=my'' \!$$   (2)


 * Based on Newton's Second Law of Motion $$ \sum F=ma $$ where  $$ a $$  is the second derivative of position with respect to time

Relations:


 * $$ f_k=ky_k \!$$  (3)


 * $$ f_c=cy_c' \!$$  (4)

Using (1) in (2)&(3):
 * $$ f_k=ky \!$$


 * $$ f_c=cy' \!$$

Then (2) becomes:

$$ f(t)=my''+cy'+ky \!$$

--Egm4313.s12.team11.arrieta 22:04, 31 January 2012 (UTC)