Good day everyone,

Until now I cannot move on with these two problems. I don't even know where to start (Crying). Anywhere, here goes:

1.) At time

*t*, a pendulum makes an angle

*x*(*t*) with the vertical axis. Assuming there is no friction, the equation of motion is

$\displaystyle mlx''(t)=-mg sin(x(t))$

where *m* is the mass and *l* is the length of the string. Use the Runge-Kutta method to solve the differential equation over the interval [0, 2] using *M =* 40 steps and *h = *0.05 if *g* = 32 ft/secē and

(a)$\displaystyle l= 3.2$ ft and $\displaystyle x(0) = 0.3$ and $\displaystyle x'(0) = 0$

(a)$\displaystyle l= 0.8$ ft and $\displaystyle x(0) = 0.3$ and $\displaystyle x'(0) = 0$

My concerns for this problem are that

(1) Am i supposed to integrate $\displaystyle mlx''(t)=-mg sin(x(x))$ so that *x''* becomes *x' *and then proceed with the iteration process?

(2) I am having a hard time trying to figure out the iteration for this problem since *x(t)* is not represented as an equation.