Modelling the System

The Apparatus is a double guided beam that can be operated in a free or a forced mode.

This continuous system is modeled by discrete spring, mass, and damping elements whose physical parameters can be denoted by:

k is the spring constant,

C is the damping constant, and

M is the effective end mass.

The spring constant for the system, k, is defined as:

(1)     

where:

k is the spring constant,

F is the static force, and

d is the displacement.

The damping coefficient, C, represents the force per unit velocity of the mass.

The effective end mass, Meff , is the equivalent point mass that accounts for the mass of the block, instruments, and beam.

The usual description of the behavior of this system is with the natural frequency and damping ratio denoted as:

= natural frequency and

= damping ratio.