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<Input>
<Text-field style="Text" layout="Normal" alignment="right" spaceabove="30"><Font bold="true" size="20">Periodicity of Sunspots</Font></Text-field>
</Input>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field bookmark="bkmrk0" style="Heading 1" layout="Heading 1">Introduction</Text-field></Title>
<Text-field style="Text" layout="Normal">This application will find the periodicity of sunspots with two separate approaches:</Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">A frequency domain transformation of the data</Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Using autocorrelation </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Both approaches should yield the same result.</Text-field>
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<Text-field bookmark="bkmrk1" style="Heading 1" layout="Heading 1">International Sunspot Data</Text-field></Title>
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<Text-field style="Text" layout="Normal">The following data table contains international sunspot numbers from the year 1701 to 2000. </Text-field>
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<Text-field style="Text" layout="Normal">The first column contains the &quot;Year&quot;, while the second column represents the &quot;Annual Mean Sunspot Number&quot;.</Text-field>
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<Text-field bookmark="bkmrk2" style="Heading 1" layout="Heading 1">Plot the Data</Text-field></Title>
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<Text-field bookmark="bkmrk3" style="Heading 1" layout="Heading 1">Periodicity via Fourier Transformation to the Frequency Domain</Text-field></Title>
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<Text-field style="Text" layout="Normal">Plot the power spectrum:</Text-field>
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<Text-field style="Text" layout="Normal">Note the peak at a frequency of 0.09 years<Font superscript="true">-1</Font> . Try zooming in and using the point probe to confirm the value of this peak frequency. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">The period is the reciprocal of the peak frequency.</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEncGVyaW9kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRLDExLjExMTExMTExRidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5">JCIrNjY2NjYhIik=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Hence, the predicted periodicity is approximately 11 years.</Text-field>
</Input>
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<Text-field style="Text" layout="Normal"></Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field bookmark="bkmrk4" style="Heading 1" layout="Heading 1">Periodicity via Autocorrelation</Text-field></Title>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Here the first peak is at 11 years, indicating that the periodicity of sunspots is approximately 11 years. This confirms the period predicted by the Fourier Transform approach.</Text-field>
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</Section><RTable 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</RTable>
</Worksheet>