A rigid circular disc of radius $r$ (in m ) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad s-1). The velocities (in $\mathrm{m} \mathrm{s}^{-1}$ ) at points O and A , respectively, are

In the context of balancing of rotating and reciprocating masses, which one of the following options is true?

A block of mass 1 kg connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is ________ (rounded off to 2 decimal places).

The system shown in the figure below consists of a cantilever beam (with flexural rigidity El and negligible mass), a spring (with spring constant $K$ and negligible mass) and a block of mass $m$. Assuming a lumped parameter model for the system, the fundamental natural frequency $\left(\omega_n\right)$ of the system is