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AP Physics 1
7.2 Frequency and Period of SHM
2.7 Kinetic and Static Friction
2.5 Newton’s Second Law
Multi-Unit
AdvancedMCQMathematicalConceptual16.3k
A horizontal baseline represents a frictionless surface. At the left end of the baseline, a vertical boundary wall is anchored. A horizontal coiled spring labeled \(k\) extends horizontally to the right from the wall and connects to the left side of a wide rectangular block labeled \(M\). Resting symmetrically on the top flat surface of block \(M\) is a smaller rectangular block labeled \(m\). The contact interface between block \(m\) and block \(M\) is horizontal. A single dashed vertical reference line extends through the center of block \(M\) to denote the equilibrium position. No other labels, lines, text, or axes appear.
A block of mass \(m\) resting on a spring-connected cart of mass \(M\).
A block of mass \(m\) is placed on top of a cart of mass \(M\). The cart is connected to an ideal horizontal spring with spring constant \(k\) and rests on a horizontal surface with negligible friction. The coefficient of static friction between the block and the cart is \(\mu_s\). The system is displaced from equilibrium and released from rest to oscillate in simple harmonic motion. What is the maximum amplitude of oscillation \(A_{\text{max}}\) for which the block will not slip on the cart, in terms of \(m\), \(M\), \(k\), \(\mu_s\), and fundamental constants?

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