An automotive engine having a mass of 135 kg is supported on 4 springs with linear characteristics. Each of the 2 front springs have stiffness of 3MN/m while the stiffness of each of 2 rear springs is 4.5 MN/m. The engine speed (rpm) at which resonance is likely to occur is
- A. 10^3 / (6 \pi)
- B. 1 / (6 \pi)
- C. 10^4 / (\pi)
- D. 10^3 / (3)
Answer: C. 10^4 / (\pi)
Explanation: Total stiffness k = 2*3 + 2*4.5 = 15 MN/m = 15*10^6 N/m. \omega_n = \sqrt{k/m} = \sqrt{15*10^6 / 135} = \sqrt{10^6 * 15/135} = 1000/3 = 333.33 rad/s. N = 60 \omega / 2\pi = 60 * (1000/3) / 2\pi = 10000 / \pi rpm.