Question

​​​​​​​Dynamics systems with vibrations. thanks

A hydrometer float, shown in figure below, is used measure specific gravity of fluids, The mass of the float is 0.0372 Kg and the diameter of the cylindrical section protruding above the surface is 0.0064 m. Determine the period of vibration when the float is allowed to bob up and down in a fluid of specific gravity 1.20. Also present the equation of motion used in this problem,

Answer 1

Soin: Given that! m= 0.0372 kg d=0.0064 m het 'n is the initial height of the cylinden immersed in water. Then the buyont force acting xv cimmensed) xg on it į 12h. Where Vo volume that immersed 2 / 2 At equilibrium, weight = bouryant force mig=12* (2 8²) хng resest Now, Let the mass be displaced by a distance in downwand direction. As a restoring force will act on the block to move it upward. The resto storing force in the boyant force. so now the forces acting are: m.g-áad?) x Ch+x) xg we know, Fama Whene, as acceleration of brock :x ma SO, mig - 2 2 2 2 2) XC htx) xg OMX pur Mag, { x ( 2 ) engl 12 ( 37 ng} * *} 0.0342 ï - Ś C &* 0.0064 +699 of Mitein, -0.000432 X = 0 CS Scanned with CamScanner

= 0.02 rad This is the homogeneous eqn of x. so, anguian Frequency - W- 10.000432 Natural frequency- 0.02 271 = 0.00318 Hz. CS Scanned with Can(Thanayan)