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AP Physics C: Mechanics
7.3 Representing and Analyzing SHM
7.1 Defining Simple Harmonic Motion (SHM)
2.8 Spring Forces
Multi-Unit
AdvancedMCQMathematicalConceptual15.8k
A side-view schematic showing a horizontal line representing a frictionless floor bounded by two vertical hatched walls on the left and right, separated by a horizontal distance labeled \(D\). Between the walls rests a rectangular block labeled \(m\). Attached to the left wall and the left face of the block is a horizontal zigzag line representing a spring labeled \(k_1, L_1\). Attached to the right face of the block and the right wall is a second horizontal zigzag line representing a spring labeled \(k_2, L_2\). Below the floor, a horizontal coordinate axis points to the right with an arrowhead labeled \(x\); a vertical tick mark aligned with the inner face of the left wall is labeled \(0\), and a vertical dashed line extends downward from the center of the block to mark its position coordinate \(x\). No other labels, lines, text, or axes appear.
Block of mass \(m\) connected between two rigid walls by two springs.
A block of mass \(m\) rests on a frictionless horizontal floor between two fixed vertical walls separated by a distance \(D\).

The block is attached to the left wall by an ideal spring with spring constant \(k_1\) and unstretched length \(L_1\), and to the right wall by an ideal spring with spring constant \(k_2\) and unstretched length \(L_2\), where \(D > L_1 + L_2\).

A coordinate system is defined along the line of motion with the origin \(x = 0\) at the left wall and the positive \(x\)-axis directed toward the right wall.

Which of the following differential equations correctly describes the position \(x(t)\) of the block?

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