Dear All,
        This is the summary for the issue on Multiple Resonance
Frequencies.
        To actuate using a square wave push-pull (with application of a dc
bias), the resulting driving force induced will have the sine of the
fundamental frequency w, followed by that of 3w, 5w, 7w, 9w and so on (all
the odd harmonics). Hence when we adjust the driving frequency towards a
higher value, and, for example, reached (1/7)w, we would be effectively
set the sine component having 7w into resonance.
Therefore, each of the increasing harmonics will resonate at a decreasing
amplitude, as depicted by their respective coefficients in the equation.

        The equation is as follows (up till the 4th harmonic)
        Veff^2 (effective potential)
        = 16*Vdc*Vac^2*(105sinwt + 35sin3wt + 21sin5wt + 15sin7wt)/105pi

        However if we only actuate the resonator using with just one end
(we set the other set of combs to be at the same potential as the mass),
we would instead observe resonance at the even integer fraction of the
fundamental frequency.

        Then the equation consist of cosine terms up to 14wt for solving
till the 4th harmonic.

        Till then, I would like to express my gratitude for those
who have responded spontaneously to the issue and in no accordance to
credit, they are

        Franck Chollet
        Richard E. Tasker
        David Ng C K
        Robert Conant
        Siddharth Kiyawat
        Roumiana Paneva
        Rajgopal Srihari
        Brandon Leow K W
        Yahong


        Thank you.

        CHUA Bee Lee
        Department of Mechanical and Production Engineering
        National University of Singapore