Homework

Homework 4 bug fixes

For the 2nd mode in problem 2, the functional form can be re-expressed (see W. Albert, 1982 reference) as:

y(x) = C₃[(0.028)sinh(qx) + sin(qx)], where q = 7.85/L and where x = 0 at the center of the beam.

The integral of y² from x = 0 to x = L/2 is: (0.250)C₃²L

The integral of (dy/dx)²from x = 0 to x = L/2 is: 11.5C₃²/ L

The integral of (d²y/dx²)²from x = 0 to x = L/2 is: 949C₃²/ L³

Here's a few worked out solutions for mode shapes:
http://www.aa.washington.edu/courses/aa312/hwk8sol.pdf
Page 13 contains results for clamped-clamped beams.

For problem 3, see the corrections to the Couette and squeeze-film damping expressions. Also, the effect of the ground plane
on the comb-drive's force can be neglected. (In practice, the polarization and small-signal voltage could be applied to the drive
combs, while the SETF and underlying electrode could be grounded. Alternatively, the SETF could be set to 5 V and the small-
signal applied to the drive comb.)

Midterm Solutions. If you have problems with the grading, please write an explanation on the cover page of the exam and submit it to either instructor for consideration.

Homework 4B (Intellisuite CAD software) Forget part (e) ... Intellisuite won't do dynamics.
Be sure to check the newsgroup for updates on various hassles with running the software.

Homework 5 Integration and Microfluidics Corrections: Problem 2b: 60 mm/s, 2c: 325 mm/s. Problem 3: Use the simplification that the flow profile is 2D with a parabolic profile across the width (flat profile across depth). Due 11/12/03.

Homework 5 Solutions