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A body is performing simple harmonic with an amplitude of 10cm. The velocity if the body was tripled by air Jet when it is at 5cm from its mean position. The new amplitude vibration is $\sqrt[]{x} c m .$ The value of x is__________.

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alok kumar singh | Contributor-Level 10

3 months ago

v = $ω \sqrt[]{A^{2} - x^{2}}$ $^{}^{}$

at x = 5, A = 10

$v' = 3 v = 3 ω \sqrt[]{A^{2} - 5^{2}} = ω \sqrt[]{A'^{2} - 5^{2}}$

$= 3 \sqrt[]{A^{2} - 5^{2}} = \sqrt[]{A'^{2} - 5^{2}}$

$\sqrt[]{1 0^{2} - 5^{2}} = \sqrt[]{A'^{2} - 25}$

$A'^{2} = 25 + 9 \times 75$ $A'^{2} = 700$

$A' = \sqrt[]{700} c m$

v = <math> <mrow> <mi>ω</mi> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math><mrow><mroot><mrow><msup><mrow></mrow><mrow></mrow></msup><msup><mrow></mrow><mrow></mrow></msup></mrow></mroot></mrow></math>at x = 5, A = 10 <math> <mrow> <mi>v</mi> <mo>'</mo> <mo>=</mo> <mn>3</mn> <mi>v</mi> <mo>=</mo> <mn>3</mn> <mi>ω</mi> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mi>ω</mi> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>3</mn> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mroot> <mrow> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mn>5</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mn>5</mn> <mo>+</mo> <mn>9</mn> <mo>×</mo> <mn>7</mn> <mn>5</mn> </mrow> </math> <math> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>7</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> <math> <mrow> <mi>A</mi> <mo>'</mo> <mo>=</mo> <mroot> <mrow> <mn>7</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow></mrow> </mroot> <mi>c</mi> <mi>m</mi> </mrow> </math>

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Answered by

alok kumar singh | Contributor-Level 10

3 months ago

v = $? \sqrt[]{A^{2} ? x^{2}}$ $^{}^{}$

at x = 5, A = 10

$v' = 3 v = 3 ? \sqrt[]{A^{2} ? 5^{2}} = ? \sqrt[]{A'^{2} ? 5^{2}}$

$= 3 \sqrt[]{A^{2} ? 5^{2}} = \sqrt[]{A'^{2} ? 5^{2}}$

$\sqrt[]{1 0^{2} ? 5^{2}} = \sqrt[]{A'^{2} ? 25}$

$A'^{2} = 25 + 9 * 75$ $A'^{2} = 700$

$A' = \sqrt[]{700} c m$

v = <math> <mrow> <mi>? </mi> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math><mrow><mroot><mrow><msup><mrow></mrow><mrow></mrow></msup><msup><mrow></mrow><mrow></mrow></msup></mrow></mroot></mrow></math>at x = 5, A = 10 <math> <mrow> <mi>v</mi> <mo>'</mo> <mo>=</mo> <mn>3</mn> <mi>v</mi> <mo>=</mo> <mn>3</mn> <mi>? </mi> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mi>? </mi> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>3</mn> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mroot> <mrow> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>? </mo> <mn>2</mn> <mn>5</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mn>5</mn> <mo>+</mo> <mn>9</mn> <mo>*</mo> <mn>7</mn> <mn>5</mn> </mrow> </math> <math> <mrow> <mi>A</mi> <msup> <mrow> <mo>'</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>7</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> <math> <mrow> <mi>A</mi> <mo>'</mo> <mo>=</mo> <mroot> <mrow> <mn>7</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow></mrow> </mroot> <mi>c</mi> <mi>m</mi> </mrow> </math>

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A body is performing simple harmonic with an amplitude of 10cm. The velocity if the body was tripled by air Jet when it is at 5cm from its mean position. The new amplitude vibration is $\sqrt[]{x} c m .$ The value of x is__________.

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A body is performing simple harmonic with an amplitude of 10cm. The velocity if the body was tripled by air Jet when it is at 5cm from its mean position. The new amplitude vibration is x c m . The value of x is__________.

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A body is performing simple harmonic with an amplitude of 10cm. The velocity if the body was tripled by air Jet when it is at 5cm from its mean position. The new amplitude vibration is $\sqrt[]{x} c m .$ The value of x is__________.