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

R1.2

Problem Statement

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

Solution

Kinematics

$\displaystyle y=y_{c}=y_{k}$ (2-0)

Kinetics

$\displaystyle r(t)=my''+f_{c}+f_{k}$ (2-1)

Where

$\displaystyle f_{k}=ky_{k}$ (2-2) and $\displaystyle f_{c}=cy_{c}$ (2-3)

Plugging into (2-1) gives us: $\displaystyle r(t)=my''+cy_{c}+ky_{k}$ (2-4)

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

$\displaystyle r(t)=my''+cy'+ky$  (2-5)