From Eqs. (2) and (3), we can know that the term about
€yg is multiplies by sin /1 or sin /2. Generally, the ground
vibration intensity is not extraordinarily strong. This
means that there is not huge vertical translation acceleration
€yg acting on the compound pendulum due to the small
angles /1 and /2. Therefore, the terms about €yg in Eqs. (2)
and (3) can be negligible. The term about _/
22
in Eq. (2) and
the terms about _/
21
; _/
1 _/
2 in Eq. (3) are all negligible as a
result of the similar reason. It demonstrates that the compound
pendulum is insensitive to vertical vibration and the
influence of vertical vibration on the compound pendulum
can be neglected.
To express directly the response characteristic of the
compound pendulum to tilt and horizontal vibration, the
expressions followed can be deduced under neglecting
above second order small quantities of Eqs. (2) and (3),