An Analysis of Forces at the Pivot Bearing of a Compound Pendulum

Abstract

Expressions for the maximum velocity and the magnitude and direction of the resultant force at the pivot bearing of a free swinging compound pendulum are developed. It is shown that the latter depend on the angle of launch, the position and the degree of compounding of the pendulum. An expression is found for the magnitude of the impulsive reaction at the pivot bearing of a compound pendulum upon impact at its perigee. It is shown that the reaction depends on the degree of compounding and place of strike of the impulse. Using a two spring analogy of stiffnesses of pendulum and impacted specimen, the maximum force on the pendulum for impact at its perigee is found to depend on the stiffnesses.