$*$Problem:$*$

A styrofoam ball is suspended in a wind tunnel. When the tunnel is turned on$,$ the ball begins to oscillate and then stabilizes at a certain height. When the tunnel is tilted, the ball moves along with it and remains at a $45\backslash$deg angle without falling.

$*$Objective:$*$

Using the damping equations of differential equations, Bernoulli, and others, you need to explain and demonstrate with formulas and mathematical justification:

$**$The initial oscillatory motion of the ball.$*$

$**$The equilibrium position of the ball.$*$

$**$The presence of damping in the system.$*$

$**$The forces acting on the ball.$*$

$**$The motion of the ball when moving and tilting the wind tunnel.$*$

$*$In other words:$*$

We are looking to build a mathematical model that describes the behavior of the styrofoam ball under different conditions in the wind tunnel. This model must consider the forces acting on the ball and explain why it behaves the way observed in the experiment.