User:Egm4313.s12.team20.stevens.t/Report 1

Given
Derive the equation of motion of a spring-dashpot in Fig.53, in K 2011 p.85, with an applied force r(t) on the ball. The figure is shown below.

Figure 2

Solution
Kinematics:
 * {| style="width:100%" border="0"|-

$$ \displaystyle y=y_k=y_c$$
 * style="width:95%" |
 * (2.0)
 * }

Kinetics:


 * {| style="width:100%" border="0"|-

$$ \displaystyle r(t)=-my''-f_k-f_c$$
 * style="width:95%" |
 * (2.1)
 * }


 * {| style="width:100%" border="0"|-

$$ \displaystyle f_k=ky_k$$
 * style="width:95%" |
 * (2.2)
 * }


 * {| style="width:100%" border="0"|-

$$ \displaystyle f_c=cy_c'$$
 * style="width:95%" |
 * (2.3)
 * }

After substituting in for $$\displaystyle y $$ with (2.1):