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

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

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

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

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

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

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