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.

| Top of the Page | back to Main Page | back to my Home Page |