An air compressor of mass (100 mathrm{~kg}) is mounted on an undamped isolator and operates at an
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An air compressor of mass \(100 \mathrm{~kg}\) is mounted on an undamped isolator and operates at an angular speed of \(1800 \mathrm{rpm}\). The stiffness of the isolator is found to be a random variable with mean value \(\bar{k}=2.25 \times 10^{6} \mathrm{~N} / \mathrm{m}\) and standard deviation \(\sigma_{k}=0.225 \times 10^{6} \mathrm{~N} / \mathrm{m}\) following normal distribution. Find the probability of the natural frequency of the system exceeding the forcing frequency.
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