Question

The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g = 10 m/s². The natural frequency of this spring-mass system (in rad/s) is _______

Answer 1

Concept:

Natural frequency is also calculated by the following formula.

\({\omega _n} = \sqrt {\frac{g}{{\rm{\Delta }}}} \)

Given:

Deflection (Δ) = 1 mm

Acceleration due to gravity (g) = 10 m/s²

Now to calculate the natural frequency we are using the formula as:

\({\omega _n} = \sqrt {\frac{g}{{\rm{\Delta }}}} \)

\(\therefore {\omega _n} = \sqrt {\frac{{10}}{{{{10}^{ - 3}}}}} \)

\(\therefore {\omega _n} = 100\;rad/s\)