Two springs of equal length but having stiffness of 10 N/mm and 15 N/mm support a mass of 2 ton in series. Find the frequency of vibration
- A. $\frac{1}{2\pi}\sqrt{3}$ Hz
- B. $\frac{1}{2\pi}\sqrt{10}$ Hz
- C. $\frac{1}{2\pi}\sqrt{15}$ Hz
- D. $\frac{1}{2\pi}\sqrt{2}$ Hz
Answer: A. $\frac{1}{2\pi}\sqrt{3}$ Hz
Explanation: Series stiffness: $1/k_{eq} = 1/10 + 1/15 \Rightarrow k_{eq} = 6$ N/mm = 6000 N/m. Mass = 2000 kg. $\omega_n = \sqrt{k/m} = \sqrt{6000/2000} = \sqrt{3}$ rad/s.