Topic: Theory of Machines
A cantilever beam of cross section A, moment of inertia I and length L is having natural frequency $omega_1$. If the beam is accidentally broken into two halves, the natural frequency of the remaining cantilever beam $omega_2$ will be such that it
- A. Increases ($omega_2 > omega_1$)
- B. Decreases ($omega_2 < omega_1$)
- C. Remains same $omega_2 = omega_1$
- D. Cannot be obtained from the given data
Answer: A. Increases ($omega_2 > omega_1$)
Explanation: For a continuous cantilever beam, the natural frequency $omega_n$ is proportional to $1/L²$. If the beam breaks and the length is halved to $L/2$, the new natural frequency will be proportional to $1/(L/2)^2 = 4/L²$, making it significantly higher. Therefore, $omega_2 > omega_1$.