I am trying to derive an equation for the oscillation of a conical float. There is a conical float with a density of delta 2 and its floating on water with density 1. Find the oscillation of the floating conical float. The final solution should be:(adsbygoogle = window.adsbygoogle || []).push({});

d^2y/dt^2=-g+(g((L-y)/L)^3)/p

where y(t) is the height of the conical float over the water, L is the length of the conical float,g is gravity and p is the ratio of the two density delta1/delta2

what i did was i found the submerge volume: (1/3)r^2(L-y)

then the weight of water displaced by the float is:

(1/3)r^2(L-y)*delta2*g

mass of float m=(1/3)r^2(L)*delta2

using this in newton's second law i got:

d^2y/dt^2=-g+g*p((L-y)/L) where p=delta1/delta2

i am not getting the solution that my professor gave?...can somebody explain where the cubed part came from?

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# Homework Help: Deriving differential eqaution

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