# E12 Labs Spring 2011

Instructor: Matt Zucker

### Lab 3

• Handout
• Excerpt from Applied Numerical Methods, by Carnahan, Luther, and Wilkes (Wiley, 1969).

### Project

The final project is intended to be an open-ended way to allow you to further investigate topics of interest from the course. It should be equivalent to roughly 1.5 labs or more in scope. You may work alone or in groups of up to three students.

Important dates:

• Friday, March 30: discuss your project idea with Professor Zucker or Professor Cheever by this day.
• Wednesday, April 4: submit a one or two paragraph project proposal to Professor Zucker via email.
• Friday, April 27: project report is due.

Here are a few project ideas (you can feel free to propose your own):

• Re-do the numerical simulation of the coupled pendulum, but eliminate some of the assumptions (small angle, no friction, linear spring, etc.).
• Analysis or synthesis of audio signals (pitch detection, pitch shifting, etc.)
• Implement an n-body gravitational simulation. Simulate the solar system.
• Learn how to derive dynamics of rigid body mechanics using the Lagrangian or Hamiltonian formulation instead of free-body diagrams.
• Implement a dynamic signal analyzer using the National Instruments A/D interfaces and MATLAB.
• Model a thermal system and compare to experimental data (we have apparatus in the lab to help with this).
• Model a triple pendulum.
• Simulate waves on the surface of water.
• Investigate basic constrols of linear systems. Make a simple PD controller for an inverted pendulum, and figure out how to tune it.
• Make a MATLAB animation of some physical system - perhaps one of the vibratory systems from earlier in the semester (the double pendulum is one example).

You can find some of these and more on Professor Cheever's project suggestions page

### Guidelines for Lab Reports

#### Sections

Your lab report should generally contain an abstract, an introduction, and sections for theory/background, procedures, results, and conclusions. The abstract (no more than a paragraph or two) should succintly introduce the objectives of the lab and summarize the results. If you have code listings longer than a few lines which you'd like to include in your report, place them in an appendix.

#### Figures and tables

Figures and tables should be clearly captioned and rendered in a professional manner. Visio, Illustrator, or the drawing tools in Word/PowerPoint, all produce reasonable figures; avoid hastily scribbled images from MS Paint. Circuits and physical systems referred to in the lab should have associated schematics and/or block diagrams. All quantities in tables (and throughout the report) should be clearly labeled with units.

#### Equations

Equations should be typeset, and numbered if they are referenced in the text, as in equation (1). You can use the equation editor in MS Word, or other tools like LaTeX or MathML to typeset your equations. When deriving theoretical explanations, make sure to justify any "tricky" steps that aren't obvious algebraic operations. See below about target audience.

#### Writing style.

Your report should be written in clear, formal language, using complete sentences. Don't mix tenses: We will do ____; We did ____. Use a consistent voice throughout the report. Make sure to proofread your report before turning it in.

#### Scope and audience

Assume your audience is knowledgable about basic topics in engineering, but not an expert in the material underlying the lab. Imagine a classmate who has not taken the course yet -- you want them to be able to walk away with a clear impression of what was done, and why it matters. The report should be self-contained: your reader shouldn't need to refer to other documents (such as the lab handout) to understand what's going on.

In terms of length: less is often more! Try to say what you need to say as efficiently as you can. Avoid repeating or paraphrasing text in multiple sections, and be extra mindful of this in light of collaborating with multiple authors.

#### What to turn in

I prefer to receive digital copies of lab reports. To turn in your lab, please email me a PDF (unfortunately, MS Word files sometimes get mangled when migrating between different versions of the program).