What stiffness should a spring be taken so that a 0.1 kg weight would oscillate freely with a period of 0.3 seconds?

As we know for sure from the school curriculum in physics, in order to determine the period of oscillation of a spring pendulum, it is necessary to use the following formula:

T = 2π * √ (m / k).

Let us determine what rigidity the spring needed to have if from the condition of our problem we know for sure that the load attached to it, whose mass is 0.1 kilogram, performed an oscillation whose period was 0.3 seconds:

0.3 = 2π * √ (0.1 / k).

0.09 = 4π ^ 2 * 0.1 / k;

k = 0.4π ^ 2 / 0.09 ≈ 43.8.

Answer: Hardness = 43.8.