University of Florida/Egm4313/s12.team8.dupre/R1.2

R1.2

Problem Statement

File:FBD1 R1.2a.jpg

Derive the equation of the spring-mass-dashpot in Fig.53 (shown above) in K 2011 p.85, with an applied force $r(t)$ on the ball.

Solution

Kinematics

$y=y_c=y_k$ (2-0)

Kinetics

$r(t)=m{y}^{″}+f_c+f_k$ (2-1)

Where

$f_k=k{y}_k$ (2-2) and $f_c=c{y}_c$ (2-3)

Plugging into (2-1) gives us: $r(t)=m{y}^{″}+c{y}_c+k{y}_k$ (2-4)

Using (2-0) and substituting into (2-4), we find that the final equation of motion for the spring-mash-dashpot is:

$r(t)=m{y}^{″}+c{y}^{\prime }+ky$  (2-5)