Homework #1
Assigned: Jan. 6th, 2005
Due: Jan. 11th, 2005
Points: 25

Please look at the practice problems before you solve this homework. Both practice problems are now solved in this pdf file now.

1. 10 points
   Read both the papers by Richard Feynman. Read them again. And again. Now, think about what aspects of his vision have come true in the field of MEMS and related areas. Choose any one aspect, research it, and discuss it briefly. For example, since 1959, has the resolving power of electron microscope gone up by a factor of 100 as he had asked? What are the limits of data storage today? Try to be unique and imaginative in your selection of the little thing you would briefly discuss. Just a few lines or a little paragraph is all you need to write.
2. 5 points
   Dimensional analysis is very useful to understand scaling effects. It is also useful when we do calculations by using scaled up or scaled down units.
   Obtain the dimensions (in terms of M (mass), L (length), T (Time), C (charge)) of magnetic flux density. In magnetics, permeability of free space is a fundamental constant. Get the dimension of that as well.
3. 10 points
   A consequence of scaling effect is that with micromechanical structures we can achieve very high natural frequencies. By taking the example of a thin circular plate clamped around the entire edge, show that it is true. Assume that the thickness of the plate is 1/50 th of its diameter, and plot the natural frequency as a function of the length scale.