- #1
mainguy
- 15
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Hi all, would appreciate a spot of help on this problem which originally comes from Feynman's introductory physics course.
1. Homework Statement
'A spar buoy of uniform cross-section floats in a vertical position with a length L submerged when there are no waves on the ocean. What is the amplitude A with respect to the mean ocean surface of the vertical motion of the uoy when there are sinusoidal waves of height h (crest to trough) and period T on the ocean? (Neglect fluid friction)
I just went for a simple differential equation, first finding an expression from:
mg = Laρg (a = area of buoy, ρ = density of water)
And rarranged to find p = m/LA
[/B]
Then from a simple differential equation
mX'' = hApgsin(wt)
Found x = hgT2/L4pi2
Where T is period.
Aaand it was wrong. Vaguely close to the real answer but I'm out by a fair bit, no idea what to correct for as there is no frictional term.
1. Homework Statement
'A spar buoy of uniform cross-section floats in a vertical position with a length L submerged when there are no waves on the ocean. What is the amplitude A with respect to the mean ocean surface of the vertical motion of the uoy when there are sinusoidal waves of height h (crest to trough) and period T on the ocean? (Neglect fluid friction)
Homework Equations
I just went for a simple differential equation, first finding an expression from:
mg = Laρg (a = area of buoy, ρ = density of water)
And rarranged to find p = m/LA
The Attempt at a Solution
[/B]
Then from a simple differential equation
mX'' = hApgsin(wt)
Found x = hgT2/L4pi2
Where T is period.
Aaand it was wrong. Vaguely close to the real answer but I'm out by a fair bit, no idea what to correct for as there is no frictional term.
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