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A cylindrical...

Question

A cylindrical disk of mass 5 kg is constrained with the two springs as shown in figure. R is radius of the disk and it rolls without slip. Determine the natural frequency for small oscillations about the mid position shown in fig. The stiffness of the each spring is 3 N/cm.

1 rad/sec

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10 rad/sec

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π rad/sec

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\frac{π}{2} rad/sec

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Solution

The correct option is A $1 rad/sec$
$\frac{3}{2} M R^{2} ¨ θ + (K {(\frac{3 R}{2})}^{2} + K {(\frac{R}{2})}^{2}) θ = 0$

$\sqrt{\frac{K_{e q}}{M_{e q}}} = 1$

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A cylindrical disk of mass 5 kg is constrained with the two springs as shown in figure. R is radius of the disk and it rolls without slip. Determine the natural frequency for small oscillations about the mid position shown in fig. The stiffness of the each spring is 3 N/cm.

The correct option is A 1 rad/sec32MR2¨θ+(K(3R2)2+K(R2)2)θ=0 √KeqMeq=1

The correct option is A $1 rad/sec$
$\frac{3}{2} M R^{2} ¨ θ + (K {(\frac{3 R}{2})}^{2} + K {(\frac{R}{2})}^{2}) θ = 0$

$\sqrt{\frac{K_{e q}}{M_{e q}}} = 1$