An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 25.7 rad/s. Calculate the distance d by which the spring stretches from its unstrained length when the object is allowed to hang stationary from it.

The distance by which the spring stretches is 1.48 cm.

Explanation:

Given that,

An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 25.7 rad/s,

We know that angular frequency in SHM is given by :

When the object is allowed to hang stationary from it, the force due to spring is balanced by its weight. Such that :

From equation (1) :

So, the distance by which the spring stretches is 1.48 cm.