Help with Mathematica: Graph Period vs Theta Not

[anonindiv]

Homework Statement

Graph in Mathematica to solve d^2theta/dt^2 + g/lsin(theta)= 0
Show a graph of period vs. Theta not.

Homework Equations

The Attempt at a Solution

I am not very experienced with entering information into mathematica. I am aware that the manipulate plot functions are probably necessary for graphing them, however after watching a number of help videos on mathematica I have failed miserably.

For instance:

Solve[{(d^2 x)/dt^2 - gsin[x] == 0}, {x, g}] is one attempt, and I realize that I mistakenly put a - instead of + sign in.

I have tried using Solve, Plot, Integrate, Dsolve...
I am simply lost.

Could anybody help me with mathematica?

Thanks,
AnonIndiv

 

[CompuChip]

Solve just solves "ordinary" equations, for differential equations use DSolve:

DSolve[x''[t] - g Sin[x[t]] == 0, x, t]

(note that you have to write the function dependence x(t) instead of x everywhere).

 

[anonindiv]

Thanks! That makes considerably more sense. But I'm still not sure how to graph the function...

 

[jackmell]

I think you need to solve an initial value problem, preferably numerically, then plot the results of that calculation. Tell you what, I'll show you how to do:

$$y''+y=0,\quad y(0)=0,\quad y'(0)=1$$

and you figure how to modify it to do yours.

mysol = NDSolve[{Derivative[2][y][t] + 
           y[t] == 0, y[0] == 0, 
       Derivative[1][y][0] == 1}, y, 
     {t, 0, 2*Pi}]
Plot[y[t] /. mysol, {t, 0, 2*Pi}, 
   PlotRange -> {{0, 2*Pi}, {-5, 5}}]

 

[anonindiv]

Thanks so much everyone!

I think I've mostly figured it out. Turns out there is a very applicable example in the mathematica database. But I rerused it and modified it sort of.

s = NDSolve[{y''[x] + 10*Sin[y[x]] == 0, y[0] == 1, y'[0] == 0},
y, {x, 0, 30}]

and then

Plot[Evaluate[{y[x]} /. s], {x, 0, 30}, PlotStyle -> Automatic].

And you get a nice graph.

Thanks all