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title: "A block of mass \\(m\\) attached to an ideal horizontal spring of spring constant \\(k\\) oscillates with amplitude \\(A\\) and period \\(T\\) on a frictionless horizontal surface. At time \\(t = 0\\), the block is released from rest at position \\(x = +A\\). Four distinct states of the block during its motion are described below:  State 1: The block is at the equilibrium position \\(x = 0\\). State 2: The magnitude of the net force acting on the block is \\(\\dfrac{1}{2}kA\\). State 3: The kinetic energy of the block is \\(\\dfrac{1}{4}E_{\\text{total}}\\), where \\(E_{\\text{total}}\\) is the total mechanical energy of the oscillator. State 4: The elapsed time since release is \\(t = \\dfrac{T}{2}\\).  Which of the following correctly ranks the magnitude of the block’s linear momentum, \\(p\\), in each state from greatest to least?"
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url: "https://nerd-notes.com/ubq/121017/"
date_modified: "2026-08-23T04:45:15+00:00"
---

# A block of mass \(m\) attached to an ideal horizontal spring of spring constant \(k\) oscillates with amplitude \(A\) and period \(T\) on a frictionless horizontal surface. At time \(t = 0\), the block is released from rest at position \(x = +A\). Four distinct states of the block during its motion are described below:

State 1: The block is at the equilibrium position \(x = 0\).
State 2: The magnitude of the net force acting on the block is \(\dfrac{1}{2}kA\).
State 3: The kinetic energy of the block is \(\dfrac{1}{4}E_{\text{total}}\), where \(E_{\text{total}}\) is the total mechanical energy of the oscillator.
State 4: The elapsed time since release is \(t = \dfrac{T}{2}\).

Which of the following correctly ranks the magnitude of the block’s linear momentum, \(p\), in each state from greatest to least?

A block of mass \(m\) attached to an ideal horizontal spring of spring constant \(k\) oscillates with amplitude \(A\) and period \(T\) on a frictionless horizontal surface. At time \(t = 0\), the block is released from rest at position \(x = +A\). Four distinct states of the block during its motion are described below:

State 1: The block is at the equilibrium position \(x = 0\).
State 2: The magnitude of the net force acting on the block is \(\dfrac{1}{2}kA\).
State 3: The kinetic energy of the block is \(\dfrac{1}{4}E_{\text{total}}\), where \(E_{\text{total}}\) is the total mechanical energy of the oscillator.
State 4: The elapsed time since release is \(t = \dfrac{T}{2}\).

Which of the following correctly ranks the magnitude of the block's linear momentum, \(p\), in each state from greatest to least?

![A schematic of a horizontal mass-spring oscillator. On the left, a vertical wall is attached to a horizontal coil spring of spring constant \(k\). The right end of the spring connects to a rectangular block of mass \(m\) resting on a horizontal floor. Below the floor, a horizontal position axis shows three vertical tick marks labeled \(-A\), \(0\), and \(+A\), with \(0\) aligned with the equilibrium position of the block. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460315-MvgtQG.jpg)

- **A.** \(p_4 > p_3 > p_2 > p_1\)
- **B.** \(p_1 > p_3 > p_2 > p_4\)
- **C.** \(p_2 > p_1 > p_3 > p_4\)
- **D.** \(p_1 > p_2 > p_3 > p_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121017/*