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Show that an undamped measuring instrument will show true response for frequency ratio.

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Show that an undamped measuring instrument will show true response for frequency ratio.

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written 5.0 years ago by |

$\frac{w}{w_n} = \frac{1}{\sqrt{2}}$ For true response, $\frac{Z}{Y} = 1$ $\therefore$ $\frac{Z}{Y} = \frac{r^2}{\sqrt{ (1-r^2)^2 + (2 \xi r)^2}}$

$1 = \frac{r^2}{\sqrt{(1-r^2)^2}}$ [ $\because$ Given undamped sys.]

$1( 1 – r^2) = r^2$

$1 – r^2 = r^2$

$1 = r^2 + r^2$

$1 = 2r^2$

$r = 1\sqrt{2}$

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