Theoretical part. In every physical pendulum it is possible to find two such points on its axis, which period of oscillations will remain constant at consecutive pinning of the

In every physical pendulum it is possible to find two such points on its axis, which period of oscillations will remain constant at consecutive pinning of the pendulum in this or that point. In our case of reversible pendulum these two points are location of prisms А and В (figure 12.2). It is possible to achieve equal oscillations periods by prisms А and B pinning of the reversible pendulum moving weights C and D on its axis:

(12.1)

where I_A and I_B – second moments of a pendulum concerning axis which pass through points A and B; a and b – spacing from the center of gravity to applicable oscillations axis. In terms of Steiner theorem:

, (12.2)

where I₀ – second moment of a pendulum concerning axis which passes through its center of gravity and which is parallel to the oscillations axis.

Substituting (12.2) in (12.1), we will get the computation formula for the free fall acceleration g:

(12.3)

Size L=a+b, which is equaled to a spacing between prisms, is named an equivalent length of a physical pendulum. Thus, for sizing of the free fall acceleration with help of reversible pendulum is necessary to measure two sizes: equivalent length L and swinging period T=T_A=T_B of physical pendulum.