A mass of 5kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

 

<p>Maximum energy = 10 J</p><p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>K</mi> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mn>0</mn> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;</p><p>K = 5</p><p>Given T_pendulum = T_spring</p><p><span contenteditable="false"> <math> <mrow> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi>m</mi> </mrow> <mrow> <mi>K</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>4</mn> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;</p><p>g = 4m/s²</p>

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