---
title: "A simple pendulum consisting of a small bob of mass \\(m\\) attached to a light string of length \\(L\\) is released from rest at an angle \\(\\theta_0\\) from the vertical, where \\(0 < \\theta_0  \\theta_0\\) (where \\(\\theta_0′ < 90^\\circ\\)). Which row in the table correctly describes how \\(T_{\\text{stat}}\\), \\(T_{\\text{dyn}}\\), and the magnitude of the time rate of change of tension \\(\\left|\\dfrac{dT}{dt}\\right|\\) at the lowest point compare to their values in the initial trial?  | | Static Component \\(T_{\\text{stat}}\\) | Dynamic Component \\(T_{\\text{dyn}}\\) | Magnitude of Rate of Change \\(\\left|\\dfrac{dT}{dt}\\right|\\) | | :— | :— | :— | :— | | (A) | Increases | Remains the same | Increases | | (B) | Increases | Increases | Increases | | (C) | Remains the same | Remains the same | Remains the same | | (D) | Remains the same | Increases | Remains the same |"
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url: "https://nerd-notes.com/ubq/124755/"
date_modified: "2026-09-28T14:10:19+00:00"
---

# A simple pendulum consisting of a small bob of mass \(m\) attached to a light string of length \(L\) is released from rest at an angle \(\theta_0\) from the vertical, where \(0 < \theta_0  \theta_0\) (where \(\theta_0′ < 90^\circ\)). Which row in the table correctly describes how \(T_{\text{stat}}\), \(T_{\text{dyn}}\), and the magnitude of the time rate of change of tension \(\left|\dfrac{dT}{dt}\right|\) at the lowest point compare to their values in the initial trial?

| | Static Component \(T_{\text{stat}}\) | Dynamic Component \(T_{\text{dyn}}\) | Magnitude of Rate of Change \(\left|\dfrac{dT}{dt}\right|\) |
| :— | :— | :— | :— |
| (A) | Increases | Remains the same | Increases |
| (B) | Increases | Increases | Increases |
| (C) | Remains the same | Remains the same | Remains the same |
| (D) | Remains the same | Increases | Remains the same |

A simple pendulum consisting of a small bob of mass \(m\) attached to a light string of length \(L\) is released from rest at an angle \(\theta_0\) from the vertical, where \(0 < \theta_0 < 90^\circ\). The tension in the string at the lowest point of the swing can be separated into a static component \(T_{\text{stat}}\) that balances the component of gravity along the string, and a dynamic component \(T_{\text{dyn}}\) that provides the centripetal acceleration. In a second trial, the pendulum is released from rest from a larger initial angle \(\theta_0' > \theta_0\) (where \(\theta_0' < 90^\circ\)). Which row in the table correctly describes how \(T_{\text{stat}}\), \(T_{\text{dyn}}\), and the magnitude of the time rate of change of tension \(\left|\dfrac{dT}{dt}\right|\) at the lowest point compare to their values in the initial trial?

| | Static Component \(T_{\text{stat}}\) | Dynamic Component \(T_{\text{dyn}}\) | Magnitude of Rate of Change \(\left|\dfrac{dT}{dt}\right|\) |
| :--- | :--- | :--- | :--- |
| (A) | Increases | Remains the same | Increases |
| (B) | Increases | Increases | Increases |
| (C) | Remains the same | Remains the same | Remains the same |
| (D) | Remains the same | Increases | Remains the same |

![A schematic diagram showing a pendulum swinging in a vertical plane. At the top center, a small horizontal hatched support attaches to a pivot point. A straight solid line of length \(L\) extends downward and to the right at an angle \(\theta_0\) to the vertical dashed line, terminating in a solid circular bob of mass \(m\). A curved arrow indicates the swing path toward the lowest point directly below the pivot, where a second circular bob is drawn with a dashed outline. At this lowest position, a vertical solid line connects the dashed bob to the pivot. A single upward arrow labeled \(T\) originates from the center of the dashed bob along the string, and a single downward arrow labeled \(mg\) originates from the center of the dashed bob. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604619-Kvi0cj.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124755/*