# GATE2016-1-37

A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $M$ and the spring constant is $K$. The polar moment of inertia for the disc about its centre is $J = \displaystyle{\frac{Ma^2}{2}}$ . The natural frequency of this system in $\text {rad} / \text {s}$ is given by

1. $\displaystyle{\sqrt{\frac{2K(a+d)^2}{3Ma^2}}} \\$
2. $\displaystyle{\sqrt{\frac{2K}{3M}}} \\$
3. $\displaystyle{\sqrt{\frac{2K(a+d)^2}{Ma^2}}} \\$
4. $\displaystyle{\sqrt{\frac{K(a+d)^2}{Ma^2}}}$

recategorized

## Related questions

A single degree of freedom spring mass system with viscous damping has a spring constant of $10$ $kN/m$. The system is excited by a sinusoidal force of amplitude $100$ $N$. If the damping factor (ratio) is $0.25$, the amplitude of steady state oscillation at resonance is ________$mm$.
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________
The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.
A slider crank mechanism with crank radius $200\:mm$ and connecting rod length $800\:mm$ is shown. The crank is rotating at $600\:rpm$ in the counterclockwise direction. In the configuration shown, the crank makes an angle of $90^\circ$ with the sliding direction of the ... of $5\:kN$ is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in $kN-m$) is __________