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NEET Physics QUESTION #1029
Question 1
In an oscillating spring-mass system, sand leaks slowly out of the box vertically as it oscillates. Which schematic correctly shows changes in average frequency \(\omega(t)\) and average amplitude \(A(t)\) with time?
  • Frequency increases (curve up), amplitude increases (curve up)✔️
  • Frequency decreases (curve down), amplitude decreases (curve down)
  • Frequency increases (curve up), amplitude stays constant (flat)
  • Frequency increases (curve up), amplitude decreases (curve down)
Correct Answer Explanation
As sand leaks out, mass decreases. \(\omega = \sqrt{k/m}\): as \(m\) decreases, \(\omega\) increases. Amplitude: since sand leaks vertically (no horizontal impulse), energy is not added but mass decreases — the amplitude increases as \(A = v_{max}/\omega\) and the system conserves momentum. Frequency increases and amplitude increases gradually.