Question

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 (in Hz) of the simple harmonic motion of a 80.0 kg diver on the board?

Answer 1

frequency in SHM is given by:

f = (1/(2*pi))*sqrt (k/m)

Here k = spring constant for diving board

Since k remains constant, So frequency of diving board is inversely proportional to the square root of effective mass on board. So

f2/f1 = sqrt (m1/m2)

f2 = f1*sqrt (m1/m2)

m1 = mass of diving board = 10.0 kg

f1 = effective frequency of empty diving board = 4.00 Hz

m2 = mass of diving board when diver on board = 80.0 + 10.0 = 90.0 kg

So,

f2 = 4.00*sqrt (10.0/90.0)

f2 = 1.33 Hz

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