The Flimsy AcceleroMeter: Analysis

Joachim Köppen DF3GJ Kiel/Strasbourg/Illkirch Winter 2004

The gravity *g* acting on the mass *M* on an arm of length *L_1*
from the pivot and under and angle *beta* against horizontal
(= rest position of instrument) produces a torque of

*
T = g M L_1 cos(beta)
*

This is balanced by the springs (of constant *D*) displaced
by *Delta x* in the horizontal direction acting on the
short arm L2 which is tilted by angle *beta* against vertical:

*
T = D Delta x L_2 = D L_2^2 sin(beta)
*

This gives for the angle *beta* of the resultant equilibrium

*
tan(beta) = g M L_2 / (D L_1)
*

For *|beta| < 30* degrees we have approximately *tan(x) = x*
within an error of
5 percent. Thus, the reading is very close to linear.

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