The load is suspended on a light vertical spring and vibrates on it with a frequency of ω = 10 rad / s, moving vertically.

The load is suspended on a light vertical spring and vibrates on it with a frequency of ω = 10 rad / s, moving vertically. How long will this spring stretch if you carefully hang the same weight to it without exciting vibrations?

1. The stiffness of the spring can be expressed as:
k = (m * g) / L;
L is the elongation of the spring under the action of the load.
2. The cyclic vibration frequency is expressed as:
w = √ (k / m) = √ (m * g / L) / m = √g / L;
3. Let us express the elongation from here:
L = g / w ^ 2 = 0.1 m = 10 cm.
Answer: L = 10 cm.