Dynamics: Pendulum Systems

Pendulum Systems

A simple gravity pendulum consists of a massless string with one end attached to a weight and the other end fixed. When an initial push is given, the pendulum will swing back and forth under the influence of gravity.

A rotational suspended system: a rigid body is suspended by two massless strings/hangers of equal length, fixed at the same point and the body rotates about the fixed point in the plane of the strings.

A translational suspended system: a rigid body is suspended by two parallel and vertical massless strings/hangers with equal length and the strings rotate about their own fixed points. Thus the rigid body moves in parallel to its static position in the plane of the strings.

• The natural frequency of a simple pendulum is independent of its mass and only relates to the length of the massless string.
• The natural frequency of a translational suspended system is independent of its mass and the location of its centre of mass and is the same as that of an equivalent simple pendulum.
• The natural frequency of a rotational suspended system is dependent on the location of its centre of mass but is independent of the magnitude of its mass.
• An outward inclinely suspended system is a mechanism. When it is loaded vertically and asymmetrically, it will move sideway and rotate.
• The lateral natural frequency of a suspended bridge estimated using simple beam theory will be smaller than the true lateral natural frequency.