A balsa wood block of mass 49 g floats on a lake, bobbing up and down at a frequ

Question

A balsa wood block of mass 49 g floats on a lake, bobbing up and down at a frequency of 2.3 Hz.
(a) What is the value of the effective spring constant of the water?
N/m
(b) A partially filled water bottle of mass 0.24 kg and almost the same size and shape of the balsa block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM.
Hz

Explanation / Answer

1) Frequency = square root(k/m)/ 2pi => 2.3 = square root(k/.049)/2pi => (2.3*2*pi)^2 *.049 = k => k = 10.23N/m 2) Frequency = square root(k/m)/ 2pi => F= square root(10.23/0.24)/(2pi) = 1.04Hz

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