Two simple harmonic motion, are represented by the equations y₁ = 10sin $\left(3\pi t+\frac{\pi }{3}\right)$ $y_2=5\left(sin3\pi t+\sqrt[]{3}cos3\pi t\right)$  

Ratio of amplitude of y₁ to y₂ = x:1. The value of x is_______ 

<p>Velocity of bob after collision, </p><p>v_{1<span contenteditable="false"> <math> <mrow> <mo>=</mo> <mroot> <mrow> <mn>5</mn> <mi>g</mi> <mi>R</mi> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mn>5</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mo>×</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>5</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span>} &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815912540"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p>From Conservation of Momentum, </p><p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>×</mo> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mo>×</mo> <mn>5</mn> </mrow> </math> </span>&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815912541"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p>-&gt;v = 400 m/s &nbsp;</p><p>&nbsp;</p>

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