---
title: "A student in a laboratory is studying two oscillating systems. System 1 consists of a block of mass \\(m\\) attached to an ideal horizontal spring of constant \\(k\\) on a frictionless surface. System 2 consists of a simple pendulum with a bob of mass \\(M\\) and a string of length \\(L\\). The original period of System 1 is \\(T_s\\) and the original period of System 2 is \\(T_p\\). The student replaces the original block in System 1 with a new block of mass \\(4m\\) and replaces the original string in System 2 with a new string of length \\(2L\\). Which of the following expressions represents the ratio of the new period of System 1 to the new period of System 2?"
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url: "https://nerd-notes.com/ubq/110893/"
date_modified: "2026-04-09T01:55:10+00:00"
---

# A student in a laboratory is studying two oscillating systems. System 1 consists of a block of mass \(m\) attached to an ideal horizontal spring of constant \(k\) on a frictionless surface. System 2 consists of a simple pendulum with a bob of mass \(M\) and a string of length \(L\). The original period of System 1 is \(T_s\) and the original period of System 2 is \(T_p\). The student replaces the original block in System 1 with a new block of mass \(4m\) and replaces the original string in System 2 with a new string of length \(2L\). Which of the following expressions represents the ratio of the new period of System 1 to the new period of System 2?

A student in a laboratory is studying two oscillating systems. System 1 consists of a block of mass \(m\) attached to an ideal horizontal spring of constant \(k\) on a frictionless surface. System 2 consists of a simple pendulum with a bob of mass \(M\) and a string of length \(L\). The original period of System 1 is \(T_s\) and the original period of System 2 is \(T_p\). The student replaces the original block in System 1 with a new block of mass \(4m\) and replaces the original string in System 2 with a new string of length \(2L\). Which of the following expressions represents the ratio of the new period of System 1 to the new period of System 2?

![Side-by-side view of two setups. On the left, System 1 shows a block of mass m attached to a horizontal spring fixed to a wall. On the right, System 2 shows a pendulum with a string of length L hanging from a ceiling with a bob of mass M at the end. Both are at equilibrium.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/setup-diagram-1775699709-fnfOUk.jpg)

- **A.** \(\dfrac{T_s}{T_p}\)
- **B.** \(\sqrt{2} \dfrac{T_s}{T_p}\)
- **C.** \(2 \dfrac{T_s}{T_p}\)
- **D.** \(2\sqrt{2} \dfrac{T_s}{T_p}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110893/*