A lobsterman\'s buoy is a solid wooden cylinder of radius r and mass M . It is w

Question

A lobsterman's buoy is a solid wooden cylinder of radius r and mass M. It is weighted on one end so that it floats upright in calm sea water, having density ?. A passing shark tugs on the slack rope mooring the buoy to a lobster trap, pulling the buoy downward a distance x from its equilibrium position and releasing it.

Show that the buoy will execute simple harmonic motion if the resistive effects of the water are neglected. (Do this on paper. Your instructor may ask you to turn in this work.)

Determine the period of the oscillations. (Use any variable or symbol stated above along with the following as necessary: g and ?.)
T =

Explanation / Answer

Let Initally the cylinder has h meter length in water

F(Buoyant Force )= weight

Let Cylinder has Cross sectional Area A

Mg = Agph

M = Ahp

Now after downward displacement by distance x

Restoring Force = - Apgx

from the Hook's law

F = - kx

k = Apg

the time period of pendulum is

T = 2pi*sqrt(M/k)

substitue the value of k , we get

T = 2pi*sqrt(M/(Apg))

since ares is A = pir^2

Therfore

T = 2pi sqrt(M/(pir^2pg))

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