- #1
drillman9
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[SOLVED] Simple Harmonic Motion - Floating Object
The problem states that an object is pushed down and released. It is floating.
The density is P(block) and the area is A and its height is h
The fluid's density is P(fluid)
The Problem asks to show that it executes simple harmonic motion with angular frequency
w = sqrt( [P(fluid)g] / [P(block)h] )
I know Fnet=ma=F(buoyancy)=(rho)(g)(V) (rho is P(block) i think)
and a = -w^2 h
and V = Ax (x is the vertical displacement of the block as its pushed down)
I rearrange the equation to get
-w^2 = ( [rho g V] / mh )
I know I must be close, but I'm not too sure how to incorporate the P(fluid) and essentially switch rho(block) from the top to the bottom
Any help would be appreciated Thanks
Homework Statement
The problem states that an object is pushed down and released. It is floating.
The density is P(block) and the area is A and its height is h
The fluid's density is P(fluid)
The Problem asks to show that it executes simple harmonic motion with angular frequency
w = sqrt( [P(fluid)g] / [P(block)h] )
Homework Equations
I know Fnet=ma=F(buoyancy)=(rho)(g)(V) (rho is P(block) i think)
and a = -w^2 h
and V = Ax (x is the vertical displacement of the block as its pushed down)
The Attempt at a Solution
I rearrange the equation to get
-w^2 = ( [rho g V] / mh )
I know I must be close, but I'm not too sure how to incorporate the P(fluid) and essentially switch rho(block) from the top to the bottom
Any help would be appreciated Thanks