A magnetic field is generated around a straight conductor, like a copper rod, when an electric current passes through it. Ampere’s Circuital Law quantifies this relationship: \[ \oint B \cdot dl = \mu_0 I, \] where \( B \) represents the magnetic field, \( \mu_0 \) is the permeability of free space, and \( I \) is the current in the conductor. The magnetic field lines are concentric circles surrounding the conductor. The direction of the field is determined by the right-hand rule: align your thumb with the current's direction; the direction your fingers curl indicates the magnetic field's direction.
In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t. Which one of the following options schematically depicts these changes correctly?