Multiple choice

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

  1. $\frac{1}{2 \pi} \sqrt{\frac{k}{m}}$
  2. $\frac{1}{2 \pi} \sqrt{\frac{2k}{m}}$
  3. $\frac{1}{2 \pi} \sqrt{\frac{2k}{3m}}$
  4. $\frac{1}{2 \pi} \sqrt{\frac{3k}{2m}}$
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C Correct answer
Explanation

Therefore, natural frequency of vibration of the system is, $$\int_n = \frac{\omega_n}{2 \pi} = \frac{1}{2 \pi} \sqrt{\frac{2k}{3m}}$$

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