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findroot problem

• To: mathgroup at smc.vnet.net
• Subject: [mg56362] findroot problem
• From: bharrison at walla.com (bruce)
• Date: Fri, 22 Apr 2005 06:25:04 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I'm new to mathematica and have been using it to solve differential
equations. Today i did a simple equation and managed to plot it (plot
looked correct) but when i tried (and tried and tried...) to use
Findroot to find the root i keep getting error messages. This is my
work (without the plot):

 mc = 1;
mp = 0.01;
l1 = 0.1;
l2 = 0.4;
g = 9.81;

d = (mc l1 - mp l2)*g/(mc l1^2 + mp l2^2)

81.1862

simpletreb = NDSolve[{ϕ''[
  t] == -d Sin[ϕ[t]], ϕ[0] == (3π/4), ϕ'[0] == 0},
ϕ[t], {t, 0, 1}]

{{&#981;[t] -> InterpolatingFunction[{{0., 1.}}, <>][t]}}

{{&#981;[t] -> InterpolatingFunction[{{0.`, 1.`}}, "<>"][t]}}

Plot[&#981;[t] /. simpletreb, {t, 0, 0.5}];

*PLOT GOES HERE*

FindRoot[&#981;[t] == 0, {t,0.2}]
  Findroot::nlnum :
   The function value (&#981;[0.2]} is not a list of numbers with
dimensions {1} at {t} = {0.2}

*************
I tried many things all of which came up with various errors. From the
plot i know the root is between 0.25 and 0.3. If anyone can point me
in right direction id greatly appreciate it!