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The period of oscillation of system shown below is $π \sqrt[]{\frac{α m}{5 k}}$ then a is _______

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alok kumar singh | Contributor-Level 10

a month ago

$k_{e q} = \frac{2 k \cdot k}{3 k} + k = \frac{5 k}{3}$

Angular frequency of oscillation $(ω) = \sqrt[]{\frac{k_{e q}}{m}}$

$ω = \sqrt[]{\frac{5 k}{3 m}}$

Period of oscillation (t) = $\frac{2 π}{ω} = 2 π \sqrt[]{\frac{3 m}{5 k}}$

$= π \sqrt[]{\frac{12 m}{5 k}}$

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820316878"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>k</mi> <mo>⋅</mo> <mi>k</mi> </mrow> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </mfrac> <mo>+</mo> <mi>k</mi> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> <mi>k</mi> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math> Angular frequency of oscillation <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>ω</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mrow> <mrow> <mi>m</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820316879"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>ω</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>5</mn> <mi>k</mi> </mrow> <mrow> <mn>3</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>            <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820316880"> </o:OLEObject></xml><! [endif]->Period of oscillation (t) = <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mi>ω</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mn>3</mn> <mi>m</mi> </mrow> <mrow> <mn>5</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1820316881"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mn>2</mn> <mi>m</mi> </mrow> <mrow> <mn>5</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>                                                   <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1820316882"> </o:OLEObject></xml><! [endif]->

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