Q. 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 $\omega(t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?
A) [image:2025p1_Q23_opt_a.png]
B) [image:2025p1_Q23_opt_b.png]
C) [image:2025p1_Q23_opt_c.png]
D) [image:2025p1_Q23_opt_d.png]
Explanation
[Solution by Claude - not from source] $\omega=\sqrt{k/m}$ increases as mass decreases. Leaking sand carries the box's instantaneous $x$ and $v$, so for the remaining mass $A^2=x^2+\frac{mv^2}{k}$ decreases as $m$ decreases. So $\omega$ rises and $A$ falls. Answer (2). (Judged from the graph shapes; verify against the official key.)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.