How to convert a low voltage (1 - 100 mV) AC signal in the range 1 - 10 Hz to DC for measurement using a DC voltmeter
There are 2 approaches that come to mind. 

1) use gravity for a reference using a simple, safe drop test with DC offset correction

2) use a calibrated accelerometer for reference and excite on a shaker table to test for linearity, bandwidth and gain/offset correction



method 1

Free-fall method with DMM that records DC offset and DC Max values

Given a drop height, h1 and a stop height, h2 with respect to to datum at contact t we get g1h1+g2h2=0 from conservation of energy.  Thus for drop g1 =-1.000...g and g2= h1/h2 [g]

Given the slope from 10% to 90% rise time , \$t_R=0.35/f_{-3dB} ~~~\$  

thus 1 to 10 Hz = 350  to 35 ms 

Depending on the range of acceleration above gravity you can choose h1/h2 = 1 and get -1g then approx +1g on the cushion for a response of  Δg=0 , -1, ~1g then bouncing until = 0 

If you want a higher g on the bounce like 10g then choose a rubber material of spring force,  k and surface area, A and mass, m to choose an appropriate material then you get an accurate Step input with a scope or sample and hold after dropping ( optical sensor) to trigger a reading. Using ΔV= Vrest-Vdrop=1.000g or 0.0000g depending if you want absolute or relative g for calibration.

The 2nd method requires a calibrated accelerometer and shaker table and DC step comparator using S&amp;H or stored Max values for + or -g on DMM.

This can be revised with your calibration error correction process.

Perhaps Method 1 is best with DC step response for a simple test and shaker table for DVT on linearity, gain, offset, hysteresis etc.

Experience

I have done as a Design/test engineer since 1976 and as Test Eng Mgr 10 yrs. later ... just like calibrating ADC for errors in gain offset then further tests for limits, linearity, monotonicity etc. for accelerometers to precise tolerances.

I used it for OCXO sensitivity (1e-11 Hz) to shock, vibe and 100g drop test 10ms as well later for shipping protection of HDD disk drives 1m drop 6 sides, 2 corners. The secret here is the fall/drop ratio of a linear spring = Δg then use random PU high density glued chip foam for low Q &lt; 5.

method 2

If you do not have a precision voltage offset supply to null DC you can make one. Most good DMM's have store Max peak readings which is useful for this test if sample rate is >30Hz measure for at least 30 cycles


  With more assumptions on your specs and test plan needs (time, accuracy, purpose e.g. design verification test DVT or production verification PVT), I can share more insight.