Atest tube is weighted by some lead shot and floats upright in a liquid of density rho. when slightly displaced from its equilibrium position and released, the test tube oscillates with shm. (a) show that the angular frequency of the oscillations is equal to √ arhog/m where g is the acceleration due to gravity, a is the cross-sectional area of the test tube and m is its mass. (b) show that the potential energy of the system is equal to 12 arhogx2 where x is the displacement from equilibrium. hence give an expression for the total energy of the oscillating system in terms of the instantaneous displacement and velocity of the test tube.