Solving a nonlinear equation numerically

I want to solve the nonlinear equation d^2(x)/dt^2 +(k)sinx = 0, numerically.

alternatively, this can be written as

Answer 1

[John D'Errico]

It looks as if you don't need to solve it numerically.

syms x(t)
xpp = diff(x,t,2)
syms k
dsolve(xpp + k*sin(x) == 0)
dsolve(xpp + k*sin(x) == 0)
ans =
                                                                   0
 2*jacobiAM((2^(1/2)*(C1 - k)^(1/2)*(C2 - t)*1i)/2, -(2*k)/(C1 - k))
-2*jacobiAM((2^(1/2)*(C1 - k)^(1/2)*(C2 - t)*1i)/2, -(2*k)/(C1 - k))

Of course, it would help if you had some initial or boundary conditions. Then you might get a better answer.

But if you really, really need to solve it numerically, then you need to start with a tool like ODE45, and you need to pose a set of initial conditions, etc. As well, you need to define the value of k. No numerical solution can be found unless you specify k as a NUMBER.

[Nivedita Tanksali]

The method that you've written the code for, what kind of method is it exactly?

as for boundary conditions,as im trying to solve the equation of motion for a nonlinear pendulum, i would think x=[0,pi/2] could be used.

The value of K is indeed a number, so that's not a problem.

[Nivedita Tanksali]

also, the initial conditions are that is, initial displacement is the amplitude

and and initial circular velocity is 0