Here we provide a selection of homework assignments templates and examples for school, college and university use. These often include a question and answer section already set out, along with space for the student name, course title, date and any other required information. Teachers and lecturers may also find these templates useful for preparing material for their classes.
In this project, students create a two-dimensional shape with nonuniform density, finds its center of mass, and hang it from a mobile. The various portion of the project address the differences and relationships between computing the center of mass of a discrete set of point masses and a lamina.
Included here is also a sample solution to help students formulate their own well-written solutions. Also, in the LaTeX code are a few comments to address some of the basics of LaTeX and Overleaf.
We will study some aspects of the damped driven pendulum. We will see that the trajectory of damped driven pendulum is unpredictable under certain ranges of parameters.
Under some conditions, the trajectory behaves like random. A perturbation of initial condition will lead to different result. Several mathematical tools will be introduced in this study.
The proof of the Dual State Lemma in Chapter 2.3 of Gilbert and Porter's Knots and Surfaces has some problems with the exposition and a critical typo. This document reworks the proof to make it more correct and comprehensible. (This material starts on page 33.)