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Derive the differential eq, governing the motion of the system, use x as the generalizing co-ordinate, assume small x and determine the natural frequency of the system.
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written 4.9 years ago by
bhaveshkumarn.pasi
• 490
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$KE = (KE)_{rod} + (KE)_M$
$= \frac{1}{2} \ IG \dot{\theta} ^2 \ + \ \frac{1}{2} \ M \ (\dot{x})^2 $
$= \frac{1}{2} [ \frac{mL^2}{12}] \ [ \frac{2 \dot{x}}{L}]^2 \ + \ \frac{1}{2} \ M{\dot{x}}^2$
$= \frac{1}{2} \ [ \frac{m}{3} + M] {\dot{x}}^2$
$PE \ = \ \frac{1}{2} \ k \ (x)^2$
$K_{eq}$ = K
$W.D. \ = \ - \int \ cy \ dy$
$y = \frac{L}{2} \ \theta = x$
$\dot{y} = \frac{L}{2} \ \dot{\theta} = \dot{x}$
= $- \int \ c \dot{x} \ dx$
$C_{eq}$ = C
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