Piston Position

Input := 

Plot[ x[t], {t,0,T},
	PlotLabel -> "Piston Position",
	AxesLabel -> {"t [sec]", "[cm]"}]

Output =

-Graphics-

Input := 

Plot[ x'[t], {t,0,T},
	PlotLabel -> "Piston Velocity",
	AxesLabel -> {"t [sec]", "[cm/sec]"}]

Output =

-Graphics-

Minimum Piston velocity

Input := 

FindMinimum[ x'[t], {t,.01}]

Output =

{-8.81697, {t -> 0.0122407}}

Maximum Piston velocity

Input := 

FindMinimum[ -x'[t], {t,.05}]

Output =

{-8.81697, {t -> 0.0477593}}

Input := 

x'[0.0477593]

Output =

8.81697

Input := 

Plot[ x''[t], {t,0,T},
	PlotLabel -> "Piston Acceleration",
	AxesLabel -> {"t [sec]", "[cm/sec^2]"}]

Output =

-Graphics-

Find minimum piston accelerations

Input := 

x''[0]

Output =

-1163.76

Find maximum piston acceleration

Input := 

FindMinimum[ -x''[t], {t,.02}]

Output =

{-613.266, {t -> 0.0367601}}

Input := 

x''[.0367601]

Output =

613.266