# 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 ${\displaystyle \displaystyle r(t)}$ on the ball.

### Solution

#### Kinematics

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

#### Kinetics

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

#### Where

${\displaystyle \displaystyle f_{k}=ky_{k}}$ (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)
```