Re: Differential Eq.
- To: mathgroup at smc.vnet.net
- Subject: [mg106534] Re: Differential Eq.
- From: dh <dh at metrohm.com>
- Date: Fri, 15 Jan 2010 03:21:44 -0500 (EST)
- References: <himsn6$j93$1@smc.vnet.net>
Hi Jamil,
g only depends on x'. We therefore define it as a function with one
parameter (== x'). It is convenient using a Piecewise function for this.
Here is the code:
===================================
b = 5;
v = 0.2;
u = 0.1;
tmax = 1;
g[der_?NumericQ] = Piecewise[{{b*v, der > v},
{b*(der - u), Abs[der - u] < v},
{-b*v, True}}];
eq = {
x''[t] - x[t] + g[x'[t]] == 0,
x[0] == 0, x'[0] == 0
};
sol = x /. NDSolve[eq, {x}, {t, 0, tmax}][[1]];
Plot[sol[t], {t, 0, tmax}, AxesLabel -> {"t", "x[t]"}]
ParametricPlot[{sol[t], sol'[t]}, {t, 0, tmax},
AxesLabel -> {"x[t]", "x'[t]"}]
=============================================
Daniel
Jamil Ariai wrote:
> Hi All,
>
>
>
> Can anybody kindly tell me how I can solve the following differential equation, with (x[0], x'[0]) = (0, 0):
>
>
>
> x''[t] -x[t] + g[t] = 0,
>
>
>
> where
>
>
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> g[t] = b*v, for x'[t] > v,
>
> g[t] = b*(x'[t]-u), for Abs[x'[t]-u] < v, and
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> g[t] = -b*v.
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>
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> Take b = 5, v = 0.2, and u = 0.1. Draw x[t] vs t, and x'[t] vs x[t].
>
>
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> Thanks.
>
>
>
> J. Ariai
>
>