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title: "A block of mass \\(m\\) is constrained to move along the horizontal \\(x\\)-axis on a frictionless surface. The block is attached to a nonlinear spring that exerts a restoring force \\(F(x) = -b x^3\\) on the block, where \\(b\\) is a positive constant and \\(x\\) is the position of the block relative to equilibrium. The block is pulled to position \\(x = x_0\\) and released from rest. Which of the following expressions represents the speed of the block as it passes position \\(x = \\dfrac{x_0}{2}\\)?"
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url: "https://nerd-notes.com/ubq/124158/"
date_modified: "2026-09-28T13:30:48+00:00"
---

# A block of mass \(m\) is constrained to move along the horizontal \(x\)-axis on a frictionless surface. The block is attached to a nonlinear spring that exerts a restoring force \(F(x) = -b x^3\) on the block, where \(b\) is a positive constant and \(x\) is the position of the block relative to equilibrium. The block is pulled to position \(x = x_0\) and released from rest. Which of the following expressions represents the speed of the block as it passes position \(x = \dfrac{x_0}{2}\)?

A block of mass \(m\) is constrained to move along the horizontal \(x\)-axis on a frictionless surface. The block is attached to a nonlinear spring that exerts a restoring force \(F(x) = -b x^3\) on the block, where \(b\) is a positive constant and \(x\) is the position of the block relative to equilibrium. The block is pulled to position \(x = x_0\) and released from rest. Which of the following expressions represents the speed of the block as it passes position \(x = \dfrac{x_0}{2}\)?

![A horizontal surface is indicated by a straight horizontal line. At the left end of the line, a vertical wall is shown as a solid vertical line. A horizontal coiled spring extends from the wall to the right, attached to a rectangular block labeled m. A horizontal coordinate axis with an arrow pointing to the right is positioned below the surface, labeled x. On this axis, three vertical tick marks are labeled from left to right as 0, \dfrac{x_0}{2}, and x_0. The center of the block is aligned with the tick mark labeled x_0. A dashed vertical line extends downward from the center of the block to the tick mark at x_0. A dashed vertical line also marks the position 0, representing the equilibrium position. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602247-Pnx6aH.jpg)

- **A.** \(x_0^2 \sqrt{\dfrac{15b}{32m}}\)
- **B.** \(x_0^2 \sqrt{\dfrac{15b}{64m}}\)
- **C.** \(x_0^2 \sqrt{\dfrac{15b}{16m}}\)
- **D.** \(x_0^2 \sqrt{\dfrac{9b}{16m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124158/*