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Solved: The period T of a simple pendulum is given by

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 5E Chapter 3.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

The period T of a simple pendulum is given by  where L is the length of the pendulum and g is the acceleration due to gravity.

a. Assume g = 9.80 m/s2 exactly, and that L= 0.742 ± 0.005 m. Estimate T, and find the uncertainty in the estimate.

b. Assume L = 0.742 m exactly, and that T = 1.73 ± 0.01 s. Estimate g, and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 5E

Step1 of 3:

Let T be the period of of a simple pendulum and it is given by

Where,

L = length of the pendulum

g = acceleration due to gravity

Here our goal is:

a).We need to Estimate T, and find the uncertainty in the estimate by Assuming g = 9.80 exactly, and that L = 0.7420.005m

b).We need to Estimate g, and find the uncertainty in the estimate by Assuming L = 0.742 m exactly, and that T = 1.730.01 s.

Step2 of 3:

a).

From the given information we have g = 9.80, L = 0.742,

Here  

mathematical constant and its value is 3.14

         

                                   =  

                       = 6.28

                     = 6.28(0.2751)

           = 1.7280

Hence,  1.7280.

Consider,

Differentiate above equation with respect to “L” we get

Let u = L/g

     du = 1/g

Apply chain rule to above equation to get a differential equation and it is given by

     

     =

  =

Substitute “u” value in above equation we get

       =

                                                 =

  =

     =

                                                 =

                                                 = 1.1645

Hence, = 1.1645.

Now,

The estimate of uncertainty is given by

 

                 = (1.1645)(0.005)

 ...

Step 2 of 3

Chapter 3.3, Problem 5E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This full solution covers the following key subjects: estimate, assume, Pendulum, uncertainty, exactly. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 5E from chapter: 3.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “The period T of a simple pendulum is given by where L is the length of the pendulum and g is the acceleration due to gravity.a. Assume g = 9.80 m/s2 exactly, and that L= 0.742 ± 0.005 m. Estimate T, and find the uncertainty in the estimate.________________b. Assume L = 0.742 m exactly, and that T = 1.73 ± 0.01 s. Estimate g, and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 71 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 5E from 3.3 chapter was answered, more than 285 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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