A string of mass per unit length $\mu$  is clamped at both ends such that one end of the string is at x = 0 and the other end at x = L. When string vibrates in fundamental mode, amplitude of the midpoint of string is a and tension is string is F. Find the total oscillation energy (in J) stored in the string.

(Use L = 1m, F = 10 N, a =   $\frac{1}{\pi }m)$

 

<p>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1819022009"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;<span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mi>F</mi> </mrow> <mrow> <mn>4</mn> <mi>L</mi> </mrow> </mfrac> <mo>=</mo> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>×</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <msup> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mfrac> <mrow> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>4</mn> <mo>×</mo> <mn>1</mn> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mo>.</mo> <mn>5</mn> <mi>J</mi> </mrow> </math> </span></p>

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