Question

The uniform solid cylinder can roll without sliding on a horizontal surface as shown in the figure. The mass of cylinder is 10 kg and spring constant for both the ideal springs is 300 N/m. The angular frequency of centre of mass of small oscillations is '2x' rad/sec. then the value of 'x'.

Answer 1

According to the concept of rolling body on horizontal surface
it is considered with respect to formula and concept of rotational and translational energy
total energy $=\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2$
$=\frac{5}{2}k{x}^2+\frac{3}{2}m{v}^2$
$\omega (=2X)=\sqrt{\frac{10k}{3m}}$
$\omega (=2X)=\sqrt{\frac{10\times 300}{3\times 10}}$
$2X=10$
$X=5$