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AP Physics C: Mechanics
7.2 Frequency and Period of SHM
IntermediateMCQMathematicalProportional Analysis20.2k
Three horizontal mass-spring configurations labeled 1, 2, and 3 stacked vertically. Configuration 1 shows a vertical hatch-lined wall on the left, a horizontal coiled spring of unstretched length L/3 attached to a square block of mass M resting on a flat horizontal floor. Configuration 2 shows an identical vertical wall on the left, a horizontal coiled spring of unstretched length 2L/3 attached to an identical square block of mass M on the flat floor. Configuration 3 shows a vertical wall on the left, a horizontal coiled spring of length L/3 attached to the left face of the square block of mass M, and a second horizontal coiled spring of length 2L/3 attached between the right face of the block and a second vertical wall on the right. No other labels, lines, text, or axes appear.
Three horizontal oscillator configurations constructed from segments of a uniform spring.
A uniform spring of unstretched length \(L\) and spring constant \(k\) is cut into two segments of unstretched lengths \(\dfrac{1}{3}L\) and \(\dfrac{2}{3}L\). Three separate horizontal oscillators are assembled on a frictionless surface using identical blocks of mass \(M\): Configuration 1 connects the block to the segment of length \(\dfrac{1}{3}L\), Configuration 2 connects the block to the segment of length \(\dfrac{2}{3}L\), and Configuration 3 places the block between two fixed walls connected to both segments on opposite sides. Which of the following correctly ranks the oscillation periods \(T_1\), \(T_2\), and \(T_3\) of the three configurations?

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