2.1 Spring-Mass System: Mass, Stiffness, Damping

A basic understanding of how a discrete spring-mass system responds to an external force can be helpful in understanding, recognising and solving many problems encountered in vibration measurement and analysis.

Figure 2.1 shows a spring-mass system. There is a mass M attached to a spring with a stiffness k. The front of the mass M is attached to a piston with a small opening in it. The piston slides through a housing filled with oil.

Figure 2.1: Spring-mass system

The holed piston sliding through an oil-filled housing is referred to as a dashpot mechanism and it is similar in principle to shock absorbers in cars.

When an external force F moves the mass M forward, two things happen:

1. The spring is stretched.

2. The oil from the front of the piston moves to the back through the small opening.

We can easily visualize that the force F has to overcome three things:

1. Inertia of the mass M.

2. Stiffness of the spring k.

3. Resistance due to forced flow of oil from the front to the back of the piston or, in other words, the damping C of the dashpot mechanism.

All machines have the three fundamental properties that combine to determine how the machine will react to the forces that cause vibrations, just like the spring-mass system.

The three fundamental properties are:

1. Mass ( M)

2. Stiffness ( k)

3. Damping ( C).

These properties are...