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Asked by brijk456 | 01 Oct, 2019, 11:21: AM
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Figure shows the cylider suspended by a spring. when a small vertical downward displacment is made,
then cylinder oscillates due to spring force (kx) and Buoyancy force [ A(L/2) d g ].  
 
When bouyancy force pushes the cylinder upwards, Spring force acts downwards.
Hence bouyancy force is in opposite direction of spring force.
 
Similar to spring force, buoyancy  force also proportional to immersed depth (L/2) in liquid.
 
Hence, effective force constant of spring due to bouyancy force  is spring constant minus Bouyance force per unit displacement.
 
Frequency f  of oscillation is given by,  
 
begin mathsize 14px style f space equals space fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator k minus left parenthesis A space d space g right parenthesis over denominator M end fraction end root end style
where k is force constant of spring, A cross section area of cylinder, d is density of liquid,
g is acceleration due to gravity and M is mass of cylinder
 
 
 
Answered by Thiyagarajan K | 02 Oct, 2019, 10:45: AM

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