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I would like to plot the following function: \begin{equation} \dot{y}=9.81\frac{90}{162.84}(e^{-\frac{162.84}{90}(t-t_0))}-1)+9.81\frac{90}{14.81}e^{-\frac{162.84}{90}(t-t_0)}(e^{-\frac{14.81}{90}t_0}-1) \end{equation} With t in the x-axis and $\dot{y}$ in the y-axis. I would like to use $t_0$ as a parameter, do you know how I can get a graph where I see what happens when I change $t_0$? Like a dynamic one if it was possible. All I could find in the documentation was the following:

ParametricPlot[{((9.81*90)/(162.84))*(Exp[-(162.84/90)*(t - r)] - 
      1) + 9.81*(90/14.81)*
    Exp[-(162.84/90)*(t - r)]*(Exp[-(14.81*r)/90] - 1)}, {r, 0, 
  50}, {t, 0, 40}]

Where I just renamed $t_0$ to $r$ to be less pedantic. Can you please help me? When I use this command, all I get is an empty frame showing the Cartesian axes.

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closed as off-topic by Bob Hanlon, MarcoB, bbgodfrey, user9660, RunnyKine Mar 6 '16 at 12:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, MarcoB, bbgodfrey, Community, RunnyKine
If this question can be reworded to fit the rules in the help center, please edit the question.

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To visualize how a function varies as a parameter varies you should become acquainted with Manipulate.

Manipulate[
  Plot[
    9.81 90/162.84 (Exp[-162.84/90 (t - r)] - 1) + 
      9.81 90/14.81 Exp[-162.84/90 (t - r)] (Exp[-14.81 r/90] - 1), 
    {t, 0, 40}],
  {r, 0, 5, Appearance -> "Labeled"}]

demo

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