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.


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

    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"}]


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