Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes times $\sqrt{2}$ as large. (c) It becomes half as large. (d) It becomes times $\frac{1}{\sqrt{2}}$ as large. (e) It remains the same.

Option (d) is the correct answer, i.e it becomes times $\frac{1}{\sqrt{2}}$ as larger.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Relationship between amplitude and length

A simple pendulum of length L can be modeled to move in simple harmonic motion for small angular displacements from the vertical. Its period is

$T = 2 π \sqrt{\frac{L}{g}}$

$T =$ Period of oscillation

$L =$ Length of pendulum

$g =$ Gravitational acceleration

Step 2: Find what will happen when its length is doubled if a simple pendulum oscillates with small amplitude

The period of a simple pendulum is

$T = 2 π \sqrt{\frac{L}{g}}$ , and its frequency is $f = \frac{1}{T} = \frac{1}{2 π} \sqrt{\frac{g}{L}}$

Thus, if the length is doubled so $l' = 2 l$ , the new frequency is

$f' = \frac{1}{T'} = \frac{1}{2 π} \sqrt{\frac{g}{L'}}$

$f' = \frac{1}{2 π} \sqrt{\frac{g}{2 L}} f' = \frac{1}{\sqrt{2}} . \frac{1}{2 π} \sqrt{\frac{g}{L}} f' = \frac{1}{\sqrt{2}} . f$

Hence option (d) is the correct answer for this question.

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Physics For Scientists & Engineers

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Short Answer

If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes times $\sqrt{2}$ as large. (c) It becomes half as large. (d) It becomes times $\frac{1}{\sqrt{2}}$ as large. (e) It remains the same.

Step by Step Solution

Step 1: Relationship between amplitude and length

Step 2: Find what will happen when its length is doubled if a simple pendulum oscillates with small amplitude

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If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes times 2 as large. (c) It becomes half as large. (d) It becomes times 12as large. (e) It remains the same.

Step by Step Solution

Step 1: Relationship between amplitude and length

Step 2: Find what will happen when its length is doubled if a simple pendulum oscillates with small amplitude

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If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes times $\sqrt{2}$ as large. (c) It becomes half as large. (d) It becomes times $\frac{1}{\sqrt{2}}$ as large. (e) It remains the same.