Good day everyone,

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

1.) At timet, a pendulum makes an anglex(t) with the vertical axis. Assuming there is no friction, the equation of motion is

wheremis the mass andlis the length of the string. Use the Runge-Kutta method to solve the differential equation over the interval [0, 2] usingM =40 steps andh =0.05 ifg= 32 ft/secē and

(a) ft and and

(a) ft and and

My concerns for this problem are that

(1) Am i supposed to integrate so thatx''becomesx'and then proceed with the iteration process?

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

2.)Predator-Prey model. An example of a system of nonlinear differential equations is the predator-prey problem. Letx(t)andy(t)denote the population of rabbits and foxes, respectively at timet. The predator-prey model asserts thatx(t)andy(t)satisfy

A typical computer simulation might use the coefficients

A = 2, B = 0.02, C = 0.0002, D = 0.8.

Use the Runge-Kutta method to solve the differential equation over the interval [0, 5] usingM= 50 steps andh =0.1 if

(a) rabbits and foxes

(b) rabbits and foxes

I basically have the same concern as the first problem. Bothx(t)andy(t)are not represented as equations, but as functions alone.

I just need someone to help me start with the two problems .