Sean-Thomas, BTW, I take great interest in your formulas, I find them very
informative. But I keep coming up with more questions as I think more about
the problem. For example, where is the end of the boom? In my case, the boom
is 38 1/4-in long tip to tip. I use a 1/4-copper plate for damping and it
hang on a L-bracket at the at the end. At the 32-inch point, the upper wire
intersects the boom. The coil and magnet are mounted at the 24 3/4-inch
point. So in your equation, L=which point? The end of the boom or the
intersection point where the guide wire is mounted?
Regards, Steve Hammond  PSN  Aptos, California

>
>Regarding Steve's question about the angles:
>
>For simplicity the horizontal pendulum has always been designed so
>that the boom and the hinge axis (either upper/lower pivots or more
>continuous flexures) are at right angles. This then makes the angle
>of the boom with respect to the horizontal the same as the angle of
>the axis of rotation with respect to the vertical, so only one variable
>angle is involved, which greatly simplifies the mathematical description
>of the pendulum. The angle of the boom and therefore the period can then
>be adjusted by tilting the base or frame along the axis of the boom, which
>is usually an external adjustment so the cover does not have to be removed.
>(The boom is often also designed to be parallel to the base or frame, which
>facilitates the alignment of magnets, coils, and transducers.)
>
>However, Since the boom or axis angle is small, sine(i) = i (radians),
>and the natural period Tn = 2*pi*sqrt(L/(g*i)). As i gets very small,
>the period gets very large. Actually, there is usually a small restoring
>moment from the hinges or pivot wires, so the boom may stay at equilibrium
>even if perfectly level. Obviously, if the mass end is raised up
>so that the boom slopes down toward the lower pivot, it will flop over
>to one side. At the other extreme, if the boom is vertical and hangs
>straight down from the hinges, it is a simple pendulum, as in the SG
design.
>
>Regards,
>Sean-Thomas
>
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