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Calculus / Fundamentals of Differential Equations 8 / Chapter 4.10 / Problem 10E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

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In the following problems, take g = 32

Chapter 4, Problem 10E

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QUESTION:

Show that the period of the simple harmonic motion of a mass hanging from a spring is \(2 \pi \sqrt{l / g}\), where $l$ denotes the amount (beyond its natural length) that the spring is stretched when the mass is at equilibrium.

Equation transcription:

$2\pi{}\sqrt{l/g}$

Text transcription:

2 pi sqrt{l / g}

Questions & Answers

QUESTION:

Show that the period of the simple harmonic motion of a mass hanging from a spring is \(2 \pi \sqrt{l / g}\), where $l$ denotes the amount (beyond its natural length) that the spring is stretched when the mass is at equilibrium.

Equation transcription:

$2\pi{}\sqrt{l/g}$

Text transcription:

2 pi sqrt{l / g}

ANSWER:

Solution :

Step 1 :

In this problem we have no find the period of simple harmonic motion.

Given that $l$ is the amount of mass stretched.

And also given that the spring is stretched which the mass is at equilibrium.

It is written has $mg=kl$

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