[1] (Dimensional Analysis) A wooden cylinder of height H and mass m floats in waler. If we give it a downward push and then let go of it, then it will start to move up and down periodically, (a) If the time for one complete up-down cycle (called the period) is a function of 1/, m and g (where g is the acceleration of gravity), use dimensional analysis to find the function (up to a dimensionless constant), (b} Suppose t also depends on A, the cross-sectional area of the wooden cylinder. Can we still use dimensional analysis alone to find the expression for ? Give some brief explanation