Question

Name: 1. (10 pts.) The equations of motion for an object moving through air with some air resis- tance are Suppose we wish to solve this using the fourth-order Runge-Kutta method and we define a vector r = (x, y, Ux, y). Write a user-defined function (e.g. like that found on p. 350 or in HW 8.3) for this problem. Be careful and note that you have two second-order equations, each of which is in two variables. 2. (10 pts. Consider the noisy data shown in the figure on the left. There does not seem to be much of a pattern to this data. The figure on the right shows the Fourier transform of this data. What do the two large peaks in the Fourier transform represent? Briefly explain.

Answer 1

I I'm sorry but as per the instructions I've been given, only first question will be answered. If consider the care of the motion of the object in air to be in projectile motion with intial ve velocity vo and the mass is m. using the second Newton law we again obtain the differential equations for x and y coordinates position of the projectile .( is expanded ag, Cl + C2).

m d’x di? C.V. -c,v: Vv? + v, dạy m -mg - cv, -cV, + v dt

2 The system can be rewritten to the four first-order equations with variables. VI = x, y2: daldt, y = y, y4 = dyldt. He obtain:

v=y, y'=-s, »V +y 1 m y3'= V4 y, '= - - m

3 Hith the initial conditions y110)-0, 4260) - Von, y360):0, 74(0) Evoy.
Please comment in case of any doubt. and please thumbs up ...i need it