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AP Physics C: Mechanics
2.8 Spring Forces
2.5 Newton’s Second Law
AdvancedMCQMathematical20.5k
A block connected to a nonlinear spring on a frictionless surface under a constant force.
A block connected to a nonlinear spring on a frictionless surface under a constant force.
A block of mass \(M\) is on a horizontal, frictionless surface and is attached to a fixed vertical wall by a nonlinear spring. The spring exerts a restoring force on the block given by \(F_s(x) = -kx - \beta x^3\), where \(x\) is the displacement of the block from the spring's equilibrium position (\(x = 0\)), and \(k\) and \(\beta\) are positive constants. The block is initially held at rest at \(x = 0\). At time \(t = 0\), a constant external horizontal force of magnitude \(F_0\) is applied to the block in the \(+x\)-direction. Which of the following expressions represents the speed \(v(x)\) of the block as a function of its displacement \(x\)?

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