Measuring the second harmonic amplitude of an oscillating torsion pendulum to detect small forces

Abstract

After more than 200 years, the torsion balance/pendulum is still one of the most precise means for measuring weak, macroscopic-range forces. Historically, two primary measurement techniques have been developed for this instrument. In one, the signal is the equilibrium angular displacement of the pendulum resulting from the presence of an external torque. In the other, this torque is detected by the associated fractional change in the natural frequency of torsion oscillations. Both techniques have been refined to the point that some experiments are now limited by temporal variations in torsion fiber temperature, despite special efforts to insure temperature stability.We have devised and tested another torsion pendulum measurement technique for which the effect of fiber temperature variations is suppressed by more than four orders of magnitude. Our observable is the amplitude of the second harmonic of the pendulum motion. A data set of 10 runs, each approximately 3 days in duration, using a magnesium/beryllium composition-dipole pendulum yielded a variation in the second harmonic amplitude of 0.29 +/- 0.47 nanoradians which corresponds to a differential acceleration between the magnesium and beryllium of 2.5 +/- 4.0 x 10--12 cm/sec2. This new technique suggests that a continued improvement in the precision of these fundamental physics experiments may be realized with a moderately high Q, room-temperature apparatus.