Introduction

• How does the solution to the exact pendulum equation of motion,
  
  differ from the solution to the approximate pendulum equation (where one makes the small angle approximation sin(Theta)~Theta)
  
  Where does the small angle approximation break down and how? In these equations, g is the acceleration due to gravity and has a value of 9.81 m/s^2.
• We will solve the equation of motion for the pendulum in the presence of damping and look at the energy of the system.

Please try running this simulation at home or in one of the CIT instructional labs. You may consult with friends, but each student is requested to run their own simulation, generate their own plots, and analyze their own results. You should read the next section very carefully before starting because it will tell you how to use the program, and how to get started.

Some semesters we may also provide computer lab sessions. You can use them to ask questions from your TA about this lab, or for running the simulations if you have trouble at home.

Each section of this lab should take no more than an hour, if you read the lab over beforehand and understand the material. Some sections demand a calculation: bring paper and pencil and a calculator. Not all sections will be assigned in all years.

• Assignment and Help
• Introduction
• Introduction to the Simulation

1. Exact vs. Approximate Solutions
2. The Damped Pendulum
3. Stable and Unstable Fixed Points

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).