A spring–mass oscillator contains sand that leaks gradually from the attached box. Which pair of schematic graphs shows how angular frequency ω(t) and amplitude A(t) evolve? Image
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Question

A spring–mass oscillator contains sand that leaks gradually from the attached box. Which pair of schematic graphs shows how angular frequency ω(t) and amplitude A(t) evolve? Image

G1 Physics · Accepted Answer

Step 1: The oscillator’s instantaneous angular frequency is ω = √(k/m). As sand escapes, effective mass m falls, while spring constant k stays fixed. Step 2: Therefore ω increases as time advances. Step 3: The escaping sand carries mechanical energy away. The remaining oscillator loses energy. Step 4: For a spring oscillator, energy E = (1/2)kA², so reducing E at fixed k reduces A. Step 5: Select the graph with increasing ω(t) and decreasing A(t). Final answer: Graph B, Option B.