The 23-kgkg disk, is pinned at its mass center OO and supports the 5-kgkg block AA. The belt which passes over the disk is not allowed to slip at its contacting surfaceDetermine the natural period of vibration of the system. The image contains a problem statement and a diagram related to mechanical vibrations, suitable for an educational website on physics or engineering.### Problem Statement"The 23-kg disk is pinned at its mass center $ O $ and supports the 5-kg block $ A $. The belt which passes over the disk is not allowed to slip at its contacting surface. (Figure 1)"### TaskDetermine the natural period of vibration of the system.Express your answer to three significant figures and include the appropriate units.**Box for Answer:** \[ \tau = \text{Value} \quad \text{Units} \]**Buttons Available:** - Submit- Previous Answers- Request Answer**Feedback:** "Incorrect; Try Again; 5 attempts remaining"### Diagram Explanation- **Disk:** A depiction of a 23-kg disk pinned at its center, labeled as $ O $.- **Block $ A $:** The 5-kg block hanging on the left side of the disk.- **Belt:** The belt passes over the disk without slipping.- **Spring:** A spring is attached on the right side with a stiffness $ k = 200 \, \text{N/m} $.- **Dimensions:** The radius to the point where the belt interacts with the disk is 300 mm.The diagram illustrates a system involving rotational and translational motion, relevant to determining the natural frequency and period of vibration.

Answered: The 23-kgkg disk, is pinned at its mass…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The 23-kgkg disk, is pinned at its mass center OO and supports the 5-kgkg block AA. The belt which passes over the disk is not allowed to slip at its contacting surface

Determine the natural period of vibration of the system.

The image contains a problem statement and a diagram related to mechanical vibrations, suitable for an educational website on physics or engineering.

### Problem Statement

"The 23-kg disk is pinned at its mass center $ O $ and supports the 5-kg block $ A $. The belt which passes over the disk is not allowed to slip at its contacting surface. (Figure 1)"

### Task

Determine the natural period of vibration of the system.

Express your answer to three significant figures and include the appropriate units.

**Box for Answer:**
\[ \tau = \text{Value} \quad \text{Units} \]

**Buttons Available:**
- Submit
- Previous Answers
- Request Answer

**Feedback:**
"Incorrect; Try Again; 5 attempts remaining"

### Diagram Explanation

- **Disk:** A depiction of a 23-kg disk pinned at its center, labeled as $ O $.
- **Block $ A $:** The 5-kg block hanging on the left side of the disk.
- **Belt:** The belt passes over the disk without slipping.
- **Spring:** A spring is attached on the right side with a stiffness $ k = 200 \, \text{N/m} $.
- **Dimensions:** The radius to the point where the belt interacts with the disk is 300 mm.

The diagram illustrates a system involving rotational and translational motion, relevant to determining the natural frequency and period of vibration.

Expert Solution

Step 1

Introduction

In this problem, we will use the equilibrium state of the disc to compute the time period of the vibrating system when the angular displacement of the disc is zero. First, we will compute the disc's mass moment of inertia and spring force, and then we will evaluate the moment at the disc's equilibrium condition.

Given data:

$\begin{array}{rcl} mass of the disk (m_{d}) & = & 23 kg \\ mass of the block (m_{b}) & = & 5 kg \\ radius of disk (r) & = & 300 mm \\ spring stiffness (k) & = & 200 N / m \end{array}$

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