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AP Physics C: Mechanics
7.3 Representing and Analyzing SHM
7.2 Frequency and Period of SHM
7.1 Defining Simple Harmonic Motion (SHM)
AdvancedMCQMathematical21k
A schematic diagram showing a horizontal spring-mass system between two vertical walls. At the far left, a vertical hatched wall is fixed to a horizontal baseline. A horizontal coil spring labeled \(k\) extends to the right from the left wall to the left face of a rectangular block labeled \(m\). From the right face of this first block, a second horizontal coil spring labeled \(4k\) extends to the left face of an identical second rectangular block labeled \(m\). From the right face of the second block, a third horizontal coil spring labeled \(k\) extends to the right to attach to a second vertical hatched wall. Both blocks rest on the flat, horizontal surface represented by a solid horizontal line. No other labels, lines, text, or axes appear.
Two identical blocks connected in series between rigid walls by three ideal springs.
Two identical blocks, each of mass \(m\), rest on a frictionless horizontal surface between two rigid vertical walls.

Block 1 is attached to the left wall by an ideal spring of spring constant \(k\), Block 2 is attached to the right wall by an identical spring of spring constant \(k\), and the blocks are connected to each other by a central ideal spring of spring constant \(4k\).

In Scenario 1, the blocks are released from rest such that their horizontal displacements from equilibrium satisfy \(x_1(t) = -x_2(t)\) at all times, whereas in Scenario 2, they are released such that \(x_1(t) = x_2(t)\) at all times.

What is the ratio of the angular frequency of oscillation in Scenario 1 to that in Scenario 2, \(\dfrac{\omega_1}{\omega_2}\)?

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