Suppose a diving board with no one on it bounces up and down in a simple harmonic motion with a frequency of 4.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 75.0-kg diver on the board?

= 1.37 Hz

Explanation:

F =

Given that

Frequency of oscillation of the empty diving board when executing Simple harmonic motion = 4.00Hz

Mass of the diving board ,m= 10kg

Mass of the person on the diving board, M = 75kg

Let k be the stiffness constant of the diving board

Let F₂ be the frequency of the board with the person on it

Frequency of the diving board F₁ =

Frequency of the diving board with the person on it  

F₂ =

Squaring both the equations and dividing the second equation with first equation

F₂² / F₁² = m / (m+M)

the frequency of the diving board with the person

F₂ =

    =

    = 1.37 Hz

the frequency of the simple harmonic motion when the diver is on the board is = 1.37 Hz

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