Differential Equations with Linear Algebra, Math 3740 Maple Assignment 2 The purpose of this notebook is to revisit Maple and use it to think about the relationship between solutions to related nth order linear differential equations. You must choose a single parter with whom to complete this assignment. This notebook has two sections. The second one contains a quiz. To receive credit, you must write explainations for your answers. You must enter explanatory text linking the Maple commands. You should be able to work the quiz by studying the examples in the preceeding sections, your first Maple assignment, and your book. This is an open-communication quiz, meaning that you may ask anyone (including your instructor, but especially your partner) for help at any time.

Define a simple ODE. To define a derivative, use the diff command. Pkkkb2RlRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSJ5R0YkNiNJInhHRiRGLUYtLCZGKiIiIyIiIkYw Solve the ODE, ode. LUknZHNvbHZlRzYiNiNJJG9kZUdGJA== Define initial conditions. PkkkaWNzRzYiNiQvLUkieUdGJDYjIiIhIiIiLy0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEYpRio= Solve ode subject to the initial conditions ics. LUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiM8JEkkaWNzR0YnSSRvZGVHRic=

For each of the following, write Maple commands linked by text explanations of what you are doing. Write your answers in a new file and include the name of your single team-mate. (a) A mass of 2 kg is attached to a spring. The mass moves by free undamped motion. The spring is stretched 3 m from its equilibrium position by a force of 24 N. Suppose that the mass is initially 1 m to the left of equilibrium and is moving left at 3 m/sec. Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (b) Suppose a dashpot that provides 8 N per m/sec resistance is attached to the system in (a). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (c) Suppose a dashpot that provides 10 N per m/sec resistance is attached to the system in (a). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (d) Suppose a dashpot that provides 6 N per m/sec resistance is attached to the system in (a). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (e) Suppose the force cos(3t) N drives the system in (b). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (f) Suppose the force cos(2t) N drives the system in (b). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (g) Suppose the force tcos(2t) N drives the system in (b). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (h) Pick a force to drive the system in (c). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (i) Pick a force to drive the system in (d). Write a differential equation that describes the motion of the mass, solve the differential equation, and graph the solution. (j) Reflect on the relationship among the solutions you found in this assignment.