---
title: "A block of mass \\(m\\) is attached to an ideal spring of spring constant \\(k\\). In System 1, the block oscillates horizontally on a frictionless surface. In System 2, the block is hung vertically from the same spring and oscillates in a uniform gravitational field of magnitude \\(g\\). Which of the following correctly compares the angular frequency \\(\\omega_2\\) of System 2 to the angular frequency \\(\\omega_1\\) of System 1, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/124235/"
date_modified: "2026-09-28T14:04:21+00:00"
---

# A block of mass \(m\) is attached to an ideal spring of spring constant \(k\). In System 1, the block oscillates horizontally on a frictionless surface. In System 2, the block is hung vertically from the same spring and oscillates in a uniform gravitational field of magnitude \(g\). Which of the following correctly compares the angular frequency \(\omega_2\) of System 2 to the angular frequency \(\omega_1\) of System 1, and provides the correct physical justification?

A block of mass \(m\) is attached to an ideal spring of spring constant \(k\). In System 1, the block oscillates horizontally on a frictionless surface. In System 2, the block is hung vertically from the same spring and oscillates in a uniform gravitational field of magnitude \(g\). Which of the following correctly compares the angular frequency \(\omega_2\) of System 2 to the angular frequency \(\omega_1\) of System 1, and provides the correct physical justification?

![A side-by-side schematic of two oscillating systems. On the left, labeled System 1, a rigid vertical wall is attached to a horizontal coil spring with stiffness labeled k, which connects to a rectangular block labeled m on a smooth horizontal floor. A double-headed horizontal arrow below the block indicates oscillation. On the right, labeled System 2, a rigid horizontal ceiling supports a vertical coil spring with stiffness labeled k, which hangs downward and connects to an identical rectangular block labeled m. A downward vertical arrow labeled g sits to the right of System 2, and a vertical double-headed arrow indicates oscillation. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604261-euMHSu.jpg)

- **A.** \(\omega_2\) is equal to \(\omega_1\) because the constant downward gravitational force shifts the equilibrium position by \(\dfrac{mg}{k}\) without changing the net restoring force per unit displacement from equilibrium.
- **B.** \(\omega_2\) is equal to \(\omega_1\) because the work done by the gravitational force over one complete oscillation cycle is zero, which keeps the total mechanical energy of the oscillator constant.
- **C.** \(\omega_2\) is greater than \(\omega_1\) because the downward force of gravity increases the magnitude of the net restoring acceleration toward equilibrium during the downward portion of the motion.
- **D.** \(\omega_2\) is less than \(\omega_1\) because the equilibrium extension of the spring increases the effective length of the oscillator, thereby increasing its period of oscillation.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124235/*