---
title: "A simple pendulum of length \\(L\\) has a period of small oscillations \\(T_0\\) inside an enclosure at rest in an inertial reference frame.  In Scenario 1, the enclosure accelerates vertically downward with a constant acceleration of magnitude \\(a\\) (where \\(a < g\\)), and the pendulum oscillates with period \\(T_1 = 2T_0\\).  In Scenario 2, the enclosure accelerates along a horizontal track with the same acceleration magnitude \\(a\\), and the pendulum oscillates with period \\(T_2\\) about its new equilibrium position.  What is the ratio \\(\\dfrac{T_2}{T_0}\\)?"
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url: "https://nerd-notes.com/ubq/124399/"
date_modified: "2026-09-28T14:05:11+00:00"
---

# A simple pendulum of length \(L\) has a period of small oscillations \(T_0\) inside an enclosure at rest in an inertial reference frame.

In Scenario 1, the enclosure accelerates vertically downward with a constant acceleration of magnitude \(a\) (where \(a < g\)), and the pendulum oscillates with period \(T_1 = 2T_0\).

In Scenario 2, the enclosure accelerates along a horizontal track with the same acceleration magnitude \(a\), and the pendulum oscillates with period \(T_2\) about its new equilibrium position.

What is the ratio \(\dfrac{T_2}{T_0}\)?

A simple pendulum of length \(L\) has a period of small oscillations \(T_0\) inside an enclosure at rest in an inertial reference frame.

In Scenario 1, the enclosure accelerates vertically downward with a constant acceleration of magnitude \(a\) (where \(a < g\)), and the pendulum oscillates with period \(T_1 = 2T_0\).

In Scenario 2, the enclosure accelerates along a horizontal track with the same acceleration magnitude \(a\), and the pendulum oscillates with period \(T_2\) about its new equilibrium position.

What is the ratio \(\dfrac{T_2}{T_0}\)?

![Two side-by-side rectangular enclosures labeled Scenario 1 and Scenario 2. In Scenario 1, an enclosure is shown with an arrow labeled a pointing vertically downward along its right outer edge. Inside, a simple pendulum hangs vertically from the ceiling with a straight line of length L ending in a small solid circle. In Scenario 2, an identical enclosure is shown with an arrow labeled a pointing horizontally to the right along its top outer edge. Inside, a vertical dashed reference line drops from the ceiling pivot, and the pendulum is shown displaced to the left at an angle from the dashed line, ending in an identical small solid circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604311-OcRXKZ.jpg)

- **A.** \(\dfrac{1}{\sqrt{5}}\)
- **B.** \(\dfrac{2}{\sqrt{7}}\)
- **C.** \(\dfrac{2}{\sqrt{5}}\)
- **D.** \(1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124399/*