---
title: "A vertical spring-mass oscillator with a block of mass \\(m\\) on an ideal spring of spring constant \\(k\\) and a simple pendulum with a bob of mass \\(m\\) on a string of length \\(L\\) both execute small-amplitude oscillations inside an elevator cab at rest on Earth. The elevator then begins accelerating upward with a constant acceleration of magnitude \\(a\\). How do the period of the spring-mass oscillator and the period of the simple pendulum in the accelerating elevator compare to their initial periods when the elevator was at rest?"
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url: "https://nerd-notes.com/ubq/122779/"
date_modified: "2026-09-28T11:02:53+00:00"
---

# A vertical spring-mass oscillator with a block of mass \(m\) on an ideal spring of spring constant \(k\) and a simple pendulum with a bob of mass \(m\) on a string of length \(L\) both execute small-amplitude oscillations inside an elevator cab at rest on Earth. The elevator then begins accelerating upward with a constant acceleration of magnitude \(a\). How do the period of the spring-mass oscillator and the period of the simple pendulum in the accelerating elevator compare to their initial periods when the elevator was at rest?

A vertical spring-mass oscillator with a block of mass \(m\) on an ideal spring of spring constant \(k\) and a simple pendulum with a bob of mass \(m\) on a string of length \(L\) both execute small-amplitude oscillations inside an elevator cab at rest on Earth. The elevator then begins accelerating upward with a constant acceleration of magnitude \(a\). How do the period of the spring-mass oscillator and the period of the simple pendulum in the accelerating elevator compare to their initial periods when the elevator was at rest?

![A rectangular outline representing an elevator cab. Suspended from the flat ceiling inside the cab are two systems side by side: on the left, a vertical coiled spring with a small square block labeled m at its bottom; on the right, a straight line of length L representing a pendulum string tilted slightly from the vertical with a circular bob labeled m at its lower end. To the right of the cab, an upward-pointing vertical arrow is labeled with a vector symbol \vec{a}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790593373-c9Cmnu.jpg)

- **A.** Spring-mass oscillator: Remains unchanged | Simple pendulum: Decreases
- **B.** Spring-mass oscillator: Remains unchanged | Simple pendulum: Increases
- **C.** Spring-mass oscillator: Decreases | Simple pendulum: Decreases
- **D.** Spring-mass oscillator: Decreases | Simple pendulum: Remains unchanged

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122779/*