# plot graph of function with different constants

I need to plot the graph of :

$$v(t) = \frac{-mg}{b} (e^{-\frac{b}{m}t}+1)$$ , where $$g = 9.8 m/s^2$$ and $$b$$ and $$m$$ are positive constants.

Is there a way to plot this without having to define random values for $$b$$ and $$m$$? I mean a way in which I can see how the graph behaves for different values of $$b$$ and $$m$$ ?

• Unfortunately no, I am new to Mathematica, I only know the basics – Physmath Apr 22 at 2:17
• I will take a look, thank you ! – Physmath Apr 22 at 2:22
• To simplify little bit, you can introduce a new variable, say $\lambda=\frac{b}{m}$. Then you can Plot a sequence of curves for a list of $\lambda$ values. – yarchik Apr 22 at 3:03

v[s_, t_] := -g/s (Exp[-s t] + 1)
g = 9.8;
slist = {0.1, 0.2, 0.4, 0.8};
Plot[Evaluate[v[#, t] & /@ slist], {t, 0, 10},
PlotTheme -> {"BoldColors", "Frame", "Grid"},
FrameLabel -> {Automatic, v[t]},
FrameStyle -> Directive[14, Black],
PlotLabels -> slist
]


• Plot[Evaluate[v[slist, t] , {t, 0, 10},...] works too. – Ulrich Neumann Apr 22 at 8:02
• @UlrichNeumann That is good suggestion, it makes the syntax more transparent. – yarchik Apr 22 at 8:12