NDSolveValue with a multiple variable equation

I'm trying to plot this equation of motion for a pendulum with a periodically applied torque for 20 cycles,

where b, m, L, g are given constant values.

periodic[tmax_,y1_,y2_,b_,m_,L_,g_,x0_,T_]:=
NDSovleValue[
{y''[t]==-(b/(m*L^2))*y'[t] - (g/L)*y[t] + T*cos{x[t]]/(m*L^2),
y'[0]==y1,
y[0]==y2,
x[0]==x0,
y,
{t,0,tmax}]

xSolution = periodic[20,Pi,1,0.22,1,1,1,1,1]

Plot[xSolution[t],{t,0.20}]


I believe Mathematica won't solve this since there are two different variables in the equation. How can I use the NDSolveValue command to solve this equation and plot the results?

• Do you have definition of x[t]? Or is it also supposed to be solved as a second differential equation? If so then what is that second equation? You also have Sovle, not Solve and a { that should probably be a [. Those are not a promising start in a language that is as demanding of correctness as Mathematica. – Bill Oct 22 '14 at 3:02
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• You can paste your code in, instead of typing it. You'll probably have fewer typos. In case it's not a type, cosine is Cos with a capital C. – Michael E2 Oct 22 '14 at 3:18
• This works, DSolve[{y''[t] == -(b/(m*L^2))*y'[t] - (g/L)*y[t] + T*Cos[Ω t]/(m*L^2), y'[0] == y1, y[0] == y2}, y, t], which is the DE you quote. Like Bill, I don't understand the role of x[t]. The equations do not completely define what x[t] equals. – Michael E2 Oct 22 '14 at 3:21
• NDSolveValue is mispelled. – lurscher Oct 22 '14 at 3:30

Your code for your model is wrong. As others are saying, your forcing function is $\cos(\omega t)$. Therefore, you simply use NDSolve to obtain solution.

eq =theta''[t] + b/(m L0^2) theta'[t] + g/L0 Sin[theta[t]] -T0 Cos[w t]/(m L0^2);
ic = {theta'[0] == Pi, theta[0] == 1};
b = 0.22;
m = 1;
L0 = 1;
g = 9.8;
w = 1;
T0 = 1;
sol = First@NDSolve[{eq == 0, ic}, theta[t], {t, 0, 10}];
Plot[theta[t] /. sol, {t, 0, 10}, PlotTheme -> "Detailed"]