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EQUIVALENT DAMPING CO-EFFICIENT.
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Damper is inclined with the direction of motion of mass:

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For actual system $F_D$ = c( $\dot{x}$ cos $\alpha$) cos $\alpha$

= $c \dot{x} \ cos^2 \ \alpha$ - - -(1)

For equivalent system

$F_D \ = \ ce \dot{x}$ - - - (2)

From equation (1) and (2)

$c_e \ = \ c \ cos^2 \ \alpha$

Dampers subjected to same velocity:

enter image description here

For actual system, damping force $F_d = f_{d1} + f_{d2}$

for equivalent system, damping force = $F_{de}$

$F_{de} = F_{d1} + F_{d2}$

$c_e \dot{x} = c_1 \dot{x} + c_2 \dot{x}$

$c_e = c_1 + c_2$

Dampers subjected to different velocity:

enter image description here

Here, net velocity of the mass is,

$x = x_1 + x_2$

$\frac{D_d}{C_e} = \frac{F_d}{C_1} + \frac{F_d}{C_2}$

$\therefore$ $\frac{1}{C_e} = \frac{1}{C_1} + \frac{1}{C_2}$

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