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

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

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

Where
$$\displaystyle f_{k}=k y_{k}$$ (2-2) and $$\displaystyle f_{c}=c y_{c}$$ (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)