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A mass on a string of unknown length oscillates as a

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics | 3rd Edition | ISBN: 9780321740908 | Authors: Randall D. Knight ISBN: 9780321740908 69

Solution for problem 19E Chapter 14

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics | 3rd Edition

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics | 3rd Edition | ISBN: 9780321740908 | Authors: Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics | 3rd Edition

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Problem 19E

Problem 19E

A mass on a string of unknown length oscillates as a pendulum with a period of 4.00 s. What is the period if

a. The mass is doubled?

b. The string length is doubled?

c. The string length is halved?

d. The amplitude is halved?

Parts a to d are independent questions, each referring to the initial situation.

Step-by-Step Solution:

Solution 19 E:

Step 1 of 1:-

The oscillation time period is given as,

.

The mass is m.

The length of the string is .

a)

If the mass is doubled, means , then what will be the time period.

We know that,

------------(1)

Where g is the acceleration due to gravity.

The above equation is independent of the mass attached with the string.

So, when the mass is doubled, the time period will remain same as 4 s.

b)

When the string length is doubled,

   

    .

So, the time period will become 5.65 s.

c)

When the string length is halved,

   

    .

So, the time period will become 2.82 s.

d)

When the amplitude is halved, the time period will be invariant. Because it is independent of the amplitude.

But if the angle increases more and we cannot take the approximation of anymore, then this formula will not hold.

Step 2 of 1

Chapter 14, Problem 19E is Solved
Textbook: Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Edition: 3
Author: Randall D. Knight
ISBN: 9780321740908

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