Homework 1, due September 4, 1013.

[goodwine]

Reading: Chapter 1 from the course text. Normally the assigned reading will closely track what we are doing in class. However, the material in Chapter 1 is of a different nature: all of it is important but some is background and some will be necessary at different times throughout the course and not all of it will seem to be connected to the next couple lectures. Again, normally this isn't the case and reading and lectures will usually closely track each other.

Exercises: 1.20, 1.21, 1.23 and 1.28 from the course text. If you need to "write a computer program to determine and approximate numerical solution" using ode45() in Matlab (or lsode() in octave) are acceptable for this assignment.

[goodwine]

Someone asked me:

For question 1.28 in the first homework set, what do you want us to turn in? Paper(s) with the equations of motion, computer code, and a graph? Or just one or two of those things? Also, what are you expecting us to write the code in? Is MATLAB ok?

I would add to that list of things a description of your interpretation of your solution. Matlab is ok for this problem.

[goodwine]

Someone asked me:

While working on Problem 1.28 (the programming question with a system of two springs and a suspended block), I was able to determine a second order differential equation to describe the change in x. I was able to solve that equation with ode45() and use the results to calculate y(t).

Is this an acceptable method of solving this problem, or do I need to also find and solve a second order diff. eq. for y? If so, how do I relate the acceleration of y to the forces acting on it if there is no mass at y0?

If your first principle analysis provides one differential equation for x and an algebraic equation for y, then you don't have to do any extra work to force y to be a differential equation. Whatever the easiest formulation for you is the best way to go unless I directly say otherwise.

[tnguye21]

For problem 1.20, do we have to write specific units like kg or seconds to describe each variable?

[goodwine]

For problem 1.20, do we have to write specific units like kg or seconds to describe each variable?

You can either use SI units or just go generic like "mass/time". The former is probably easier.

[klalka]

For Problem 1.23, what do the pictures with the mechanisms labeled "b" represent?

[goodwine]

For Problem 1.23, what do the pictures with the mechanisms labeled "b" represent?

That's a damper. It's described in Chapter 1.

[jkearns]

For Problem 1.20, is a second order differential equation, one that represents the acceleration of the rope, sufficient to answer the problem statement? As in, is an equation for acceleration sufficient to satisfy the prompt for "an equation of motion?"

[goodwine]

For Problem 1.20, is a second order differential equation, one that represents the acceleration of the rope, sufficient to answer the problem statement? As in, is an equation for acceleration sufficient to satisfy the prompt for "an equation of motion?"

Yes.