Topic: Theory of Machines
If the length of the cantilever beam is reduced to 1/4th, the natural frequency of the mass M at the end of this cantilever beam of negligible mass will be increased by a factor of
- A. 2
- B. $\sqrt{8}$
- C. 4
- D. 8
Answer: D. 8
Explanation: Deflection delta = (Mg*L³)/(3EI). Natural frequency f is proportional to 1/$\sqrt{delta}$, which means f is proportional to 1/L^(3/2). f2/f1 = (L1/L2)^(3/2) = (L / (L/4))^(3/2) = 4^(3/2) = 8.