A vibrating system consists of a mass of 200 kg, spring stiffness of 80 N/mm. The natural frequency of vibration of the system is

Concept:

The natural frequency of a spring-mass system is given by,

 and 

where k = spring stiffness (N/m) and m = mass of the body (kg)

Calculation:

Given:

Mass of body (m) = 200 kg, spring stiffness (k) = 80 N/mm = 80 × 10³ N/m

The natural frequency of vibration is:

Confusion Points

Based on the units of answer we have to use the formula. If we use  the answer will be in Hertz or s^-1. 

Mistake Points

Use SI unit while calculating natural frequency.

As per the given units, the answer will not come so first we have to convert it into SI unit.