For this assignment, you will be asked to simulate a system in MATLAB. In other words, you will solve  differential equations by computer rather than by hand. This is not meant to be difficult, but to give you a taste of something practical outside of the classroom. I have chosen MATLAB because I find it to be easiest and common in engineering. If you have an intense desire to complete this assignment in a software or programming language other than MATLAB, let me know.

Introduction

As an NYU student, you can install MATLAB for free at

https://www.mathworks.com/products/matlab/student.html.

An installation of MATLAB also includes the easy-to-use simulation tool Simulink.

openExample('simulink_general/sldemo_bounceExample')

If you run the above command in MATLAB, it will open up a simulation of a bouncing ball in Simulink. [https://www.mathworks.com/help/simulink/slref/simulation-of-a-bouncing-ball.html]

This example illustrates the solution of a second-order differential equation with constant coefficients and discontinuous (or hybrid) dynamics. The second-order differential equation is due to the system dynamics of free fall governed by Newton’s second law and the discontinuous dynamics arise from ground collision.

Other resources for your reference:

Simulink On-ramp:https://matlabacademy.mathworks.com/details/simulink-onramp/simulink

MATLAB On-ramp:https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

Problem Statement:

A handball of mass 0.065 kg is dropped from rest at a height of 25 m. The magnitude of the force of air resistance on the handball is 2/1 Cd ρAv2 , where the drag coefficient Cd = 0.47 (for a sphere), density of air ρ =  1.293 kg/m3, cross-sectional area A = 0.025 m2, and v is the velocity. Note that the direction of air resistance is always opposite the motion of the handball. The acceleration due to gravityg = 9.81     m/s2 and the coefficient of restitution κ = 0.9.