Question

A disc of mass m is attached to a spring of stiffness k as shown in the fig, The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

• A. $\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
• B. $\frac{1}{2\pi }\sqrt{\frac{2k}{m}}$
• C. $\frac{1}{2\pi }\sqrt{\frac{2k}{3m}}$
• D. $\frac{1}{2\pi }\sqrt{\frac{3k}{2m}}$

Answer 1

The correct option is C $\frac{1}{2\pi }\sqrt{\frac{2k}{3m}}$

$I\dot{\theta }+kxr=0$

$(\frac{m{r}^2}{2}+m{r}^2)\ddot{\theta }+K(r.\theta )r=0$

$\frac{3}{2}m{r}^2+K{r}^2\theta =0$

$\ddot{\theta }+\frac{2K}{3m}\theta =0$

$\text{Natural frequency}=\frac{1}{2\pi }\sqrt{\frac{2k}{3m}}$