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The period T of a simple pendulum is given by where L is

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

Solution for problem 8E Chapter 3.2

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 8E

The period  of a simple pendulum is given by \(T=2 \pi \sqrt{L / g}\) where  is the length of the pendulum and  is the acceleration due to gravity. Thus if  and  are measured, we can estimate  with \(g=4 \pi^{2} L / T^{2}\). Assume that the period is known to be \(T=1.5 \mathrm{~s}\) with negligible uncertainty, and that  is measured to be \(0.559 \pm 0.005 \mathrm{~m}\). Estimate , and find the uncertainty in the estimate.

Equation Transcription:

Text Transcription:

T=2{pi}sqrt{L/g}

g=4{pi}^{2}L/T2

T=1.5 s

0.559{+/-}0.005 m

Step-by-Step Solution:

Solution :

Step 1 of 1:

Let the period perod of a simple pendulum is given by

Where,

L = length of the pendulum and

g = acceleration due to gravity.

So m

Here L=0.559 and m

We assume that the the period is  T=1.5 s.

Our goal is :

We need to estimate g and the uncertainty in the estimate.

Now we have to find the estimate of g and the uncertainty in the estimate.

The formula of the acceleration is given by

We know that L and T values.

Therefore the acceleration due to gravity is .

Now we have to find the estimate of the uncertainty.

Consider,

Differentiate above equation with respect to “L” we get

Here we substitute and T values.

 

Hence .

Now,

The estimate of uncertainty is given by

Here m.

Hence .

Therefore, The estimate of uncertainty is g = 9.80810.0087  


 

Step 2 of 1

Chapter 3.2, Problem 8E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “?The period of a simple pendulum is given by \(T=2 \pi \sqrt{L / g}\) where is the length of the pendulum and is the acceleration due to gravity. Thus if and are measured, we can estimate with \(g=4 \pi^{2} L / T^{2}\). Assume that the period is known to be \(T=1.5 \mathrm{~s}\) with negligible uncertainty, and that is measured to be \(0.559 \pm 0.005 \mathrm{~m}\). Estimate , and find the uncertainty in the estimate.Equation Transcription:Text Transcription:T=2{pi}sqrt{L/g}g=4{pi}^{2}L/T2T=1.5 s0.559{+/-}0.005 m” is broken down into a number of easy to follow steps, and 78 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: estimate, period, uncertainty, Pendulum, measured. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 8E from chapter: 3.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 8E from 3.2 chapter was answered, more than 306 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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The period T of a simple pendulum is given by where L is