Suppose a diving board with no one on it bounces up and down in a simple harmonic motion with a frequency of 6.90 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 67.6 kg diver on the board?

The frequency of the simple harmonic motion of a 67.6 kg diver on the board = 2.48 Hz

Explanation:

The frequency in simple harmonic motion is related to spring constant and mass causing the motion through the relation

f = (1/2π) √(k/m)

When mass = 10 kg, f = 6.90 Hz,

6.9 = (1/2π) √(k/10)

(√(k/10) = 6.9×2π = 43.354

k/10 = 43.354² = 1879.57

K = 18795.7 N/m

When a diver of mass 67 kg climbs the diving board, the total mass on the diving board now becomes (10+67.6) = 77.6 kg

Spring constant of the diving board doesn't change,

So, the frequency is then given by

f = (1/2π) √(18795.7/77.6)

f = 2.48 Hz