Page 256 - Gas Adsorption Equilibria

242 Chapter 5

The coefficient of internal damping of the wire included in Eq. (5.1) in
practice must be determined from calibration experiments with either the
empty or the loaded pendulum in vacuum, cp. Eq. (5.12). Experiments have
shown that may change over the years which can be due to irreversible
plastic deformation or corrosion if measurements in chemically aggressive
sorptive gases have been performed [5.2].

After the fading away of initial disturbances the motion of the rotational
pendulum in vacuum always can be described by a simple damped harmonic
oscillation. For initial conditions we have for the angular
amplitude

Here is the initial amplitude of the pendulum, is the angular
frequency with indicating the period of the oscillations. The parameter
is the logarithmic decrement defined by the relation as

The frequency and decrement are related to the parameters of the
pendulum by the equations

Conversely, we have from (5.9, 5.10)