Answered: The 25-lb block is attached to two…

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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Question

The 25-lb block is attached to two springs having a stiffness of k = 14 lb/ft . A periodic force F=(8cos3t)lb, where t is in seconds, is applied to the block.

Determine the maximum speed of the block after frictional forces cause the free vibrations to dampen out.

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

### Problem Description

The 25-lb block is attached to two springs having a stiffness of \( k = 14 \, \text{lb/ft} \). A periodic force \( F = (8 \cos 3t) \, \text{lb} \), where \( t \) is in seconds, is applied to the block. ([Figure 1](#))

### Objective

Determine the maximum speed of the block after frictional forces cause the free vibrations to dampen out.

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

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### Figure Description

The figure illustrates a block connected to two springs. Each spring has a stiffness labeled as \( k \). There is a periodic force \( F = 8 \cos 3t \) acting horizontally on the block.

The setup suggests a classic mass-spring system encountering a periodic external force, demonstrating forced vibrations.

### Solution Input

To submit your solution, use the following format for the maximum speed:
\[
(v_p)_{\text{max}} = \text{Value (units)}
\]
Submit your answer for evaluation.

[Submit](#Submit)
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Expert Solution

Step 1

Given data

Weight of block = 25 lb

Stiffness constant = 14 lb/ft

Find the maximum speed .

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