These are not only sensitive to translational but also to angular acceleration. The rotational component of seismic shear waves is however too small to have a noticeable effect; its contribution to the output signal is of the order kl where k is the horizontal wavenumber and l the length of the pendulum [Rodgers 1969]. In technical applications or on a shake table, effects of rotation may be noticeable.
For small translational ground motions, the equation of motion of a rotational pendulum is formally identical to eq. (2) but z must then be interpreted as the angle of rotation. Since the rotational equivalents to the constants M, R, and S in eq. (2) are of little interest in modern force-balance seismometers, we will not discuss them further and refer the reader instead to the older literature [Berlage Jr. 1932].