A ball weighing 100 grams, suspended from a spring, makes 30 vibrations per minute. Determine the stiffness of the spring.

Oscillation period (per second) through spring rate:

T = 2 * π * √ (m / k), where m is the mass of the ball in kg, m = 0.1 kg, k is the stiffness of the spring in N / m.

From this formula, we express the spring stiffness k:

(T / (2 * π)) ^ 2 = m / k;

k = m / (T / (2 * π)) ^ 2 = (4 * π ^ 2 * m) / T ^ 2, where T = t / N, t is the oscillation time.

Then,

k = (4 * π ^ 2 * m * N ^ 2) / t ^ 2 = (4 * (3.14) ^ 2 * 0.1 * 30 ^ 2) / (60) ^ 2 = (4 * (3.14) ^ 2 * 0.1) / 4 =

= (3.14) ^ 2 * 0.1 = 9.8596 * 0.1 = 0.98596 N / m ≈ 0.986 N / m.

Answer: spring rate k = 0.986 N / m.