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AP Physics C: Mechanics
7.4 Energy of Simple Harmonic Oscillators
7.2 Frequency and Period of SHM
AdvancedMCQMathematicalProportional Analysis16k
A horizontal spring-mass system resting on a horizontal surface. On the left is a vertical wall shown with diagonal hash marks along its left boundary. A horizontal helical spring extends from the wall to a square block of mass \(M\) on the right. The block rests on a horizontal line representing a frictionless floor. Above the spring, a horizontal double-headed dimension arrow spans the full length of the spring from the vertical wall to the left face of the block, labeled \(L\). A horizontal axis below the floor has an origin tick labeled 0 at the wall and points to the right with an arrow labeled \(x\). No other labels, lines, text, or axes appear.
Horizontal spring-mass oscillator on a frictionless surface.
An experiment is designed to determine the angular frequency \(\omega\) of a horizontal oscillator consisting of a block of mass \(M\) attached to a spring of force constant \(k\), length \(L\), and uniform mass \(m_s\). The block is released from rest from various displacement amplitudes \(A\) along a frictionless horizontal track, and its maximum speed \(v_{\text{max}}\) is recorded for each trial. Each element of the spring at a distance \(x\) from its fixed end moves with speed \(v(x) = \left(\dfrac{x}{L}\right)v\), where \(v\) is the instantaneous speed of the block. If the student plots \(v_{\text{max}}\) on the vertical axis as a function of \(A\) on the horizontal axis, which of the following correctly identifies the theoretical slope of the best-fit line and the effect of the spring's mass on the graph compared to that of an ideal massless spring?

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