Notations and units:

= mass, = stiffness, = acceleration due to gravity, = modulus of elasticity, = load, = mass, = amplitude, = number of cycles

Units of the notations are in SI units.

Frequency = 1/ Time period

Natural frequency

Natural frequency considering inertia

= mass of spring

Circular frequency

Deflection of longitudinal vibrations

Equivalent stiffness when spring are connected in series

Equivalent stiffness when spring are connected in parallel

When spring is cut into “n” parts, stiffness of each cut spring becomes “nk”, where k= stiffness of spring before cutting.

Damping coefficient = Damping force / velocity

Damping factor or damping ratio

Critical damping coefficient

Circular frequency of damped vibration

= 0 – Critically damped

< 1 – Under damped

> 1 – Over damped

Logarithmic decrement