Topic: Vibrations
A cantilever beam of length 'L' has natural frequency ω₁. If the beam is broken into halves, the natural frequency of the remaining cantilever beam ω₂ will be such that
- A. ω₂ < ω₁
- B. ω₂ > ω₁
- C. ω₂ = ω₁
- D. Cannot be obtained from the given data
Answer: B. ω₂ > ω₁
Explanation: Natural frequency ω is proportional to √(k/m). Stiffness k of a cantilever is proportional to EI/L³. If L becomes L/2, stiffness k becomes 8 times the original. Frequency is proportional to √k, so it increases. ω is inversely proportional to L², so halving the length increases the frequency by a factor of 4. The provided solution notes ω ∝ 1/L^(3/2), which also leads to an increase.