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Find the maximum permissible unbalanced in order to limit the steady state deflection to 5mm peak to peak.
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A centrifugal pump, weighing 60N and operating at 1000 rpm, is mounted on six springs of stiffness 600 ON/m each, Find the maximum permissible unbalanced in order to limit the steady state deflection to 5mm peak to peak.

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$m = \frac{600}{9.81} = 61.16$ kg

$w = \frac{2 \pi N}{60} = \frac{2 \pi \times 1000}{60}$

W = 104.72 rad/sec.

Number of springs = 6

$K_{eq}$ = 6k

Mo.e = ?

$\therefore$ $X = 2.5mm = 2.5 \times 10^{-3} \ m$

No damper $\therefore \zeta = 0$

$\frac{X}{\frac{mo.e}{m}} = \frac{r^2}{\sqrt{(1-r^2)^2}}$

$\therefore$ $Wn = \sqrt{ \frac{Keq}{m}}$

$= \sqrt{ \frac{ 6 \times 6000}{61.16}}$

Wn = 24.26 rad/sec.

$r = \frac{w}{Wn} = \frac{104.72}{24.26} = 4.316$

$\frac{2.5 \times 10^3}{\frac{mo.e}{61.16}} = \frac{(4.316)^2}{\sqrt{(1 – (4.316)^2)^2}}$

$= \frac{18.63}{17.63}$

$= 1.0566 \times \frac{mo.e}{61.16}$

Mo.e = 0.14469 kg m

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