Question #43924

This question tests the understanding of dry friction damping (Coulomb damping) in an oscillating system.

A common misconception is applying the work-energy theorem by assuming the block comes to a permanent rest exactly at the unstretched position ($x=0$), leading to the incorrect equation $\frac{1}{2} k_{eff} x_0^2 = \mu_k m g D$ (Option C).

In reality, the equilibrium position shifts by $\pm \frac{\mu_k m g}{k_{eff}}$ depending on the velocity direction, causing the amplitude to decay in an arithmetic progression.

Furthermore, students must check the static friction condition at the end of each half-cycle to determine the exact stopping point, rather than assuming continuous energy dissipation.