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AP Physics C: Mechanics
7.3 Representing and Analyzing SHM
AdvancedMCQMathematical14.2k
A block of mass m rests on a horizontal line representing a frictionless surface. A horizontal spring with spring constant k connects the left side of the block to a vertical wall on the left. A horizontal arrow labeled F(t) points to the right from the right side of the block. A horizontal position axis x extends to the right below the surface, with an origin marked x = 0 directly beneath the center of the block. No other labels, lines, text, or axes appear.
A mass-spring system subjected to a time-dependent driving force.
A block of mass \(m\) on a frictionless horizontal surface is connected to a rigid wall by an ideal spring of spring constant \(k\). An external driving force \(F(t) = F_0 \cos(\omega t)\) is applied to the block, where \(F_0\) and \(\omega\) are positive constants. The differential equation governing the motion of the block is \(m \dfrac{d^2x}{dt^2} + kx = F_0 \cos(\omega t)\). Assuming a steady-state solution of the form \(x(t) = A \cos(\omega t)\), where \(\omega \ne \sqrt{\dfrac{k}{m}}\), which of the following expressions represents the steady-state amplitude \(A\) of the oscillation?

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