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Crystal oscillator - Wikipedia

A crystal oscillator is an electronic oscillator circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal ...

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Physics Notes on Units and Measurement for CBSE Class 11

Jun 16, 2017 ... Class 11 Physics notes on Units & Measurement (Chapter 2 of 11th ... Error, Relative Error and Percentage Error, Combination of Errors, ... The result of every measurement by any measuring instrument contains some uncertainty. ... Least count error belongs to the category of random errors but within a ...

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The relative error in a physical quantity raised to the power k is equal to k times the individual quantity's relative error.

Z = \frac{A^p B^q}{C^r}

\frac{\Delta Z}{Z} = p \frac{\Delta A}{A} + q \frac{\Delta B}{B} + r \frac{\Delta C}{C}

Given that

Time period of oscillations T = 2\pi \sqrt{\frac{L}{g}}   

Length L = 20 cm

Least count error of length \Delta L = 1 mm = 0.1 cm

Time period of oscillations t = 90 sec

Least count error of time \Delta t = 1 sec

Step 1: Set up an equation for g

T = 2\pi \sqrt{\frac{L}{g}}

Square on both sides

T^2 = 4\pi^2 \frac{L}{g}

g = 4\pi^2 \frac{L}{T^2}

Relative error \frac{\Delta g}{g} = \frac{\Delta L}{L} + 2 \frac{\Delta T}{T} ...................(1)

Time taken for n oscillations = t

Time taken for 1 oscillation = ?

Time period one oscillation T = \frac{t}{n}

Error \Delta T = \frac{\Delta t}{n}

We can write, \frac{\Delta T}{T} = \frac{\Delta t}{t}

Substitute \frac{\Delta T}{T} value in equation (1)

Hence, Relative error \frac{\Delta g}{g} = \frac{\Delta L}{L} + 2 \frac{\Delta t}{t}

Step 2: Finding the relative and percentage error

Relative error \frac{\Delta g}{g} = \frac{0.1}{20} + 2 \frac{1}{90}

Relative error \frac{\Delta g}{g} = 0.027

Percentage error \frac{\Delta g}{g} * 100 = 0.027 * 100

Percentage error = 2.7 % \approx3%

Therefore, Accuracy in  determination of g = 3%