A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a single node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2

A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a single node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2 Correct Answer 171

For a single node system, the node occurs at a distance 1.146m from left end. The polar moment of inertia = 2.36×106 m4 La = 0.4356m (from same frequency relation) Substituting these values into the frequency relation we get f = 171 Hz.
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Modern civilization is completely dependent on energy, which has therefore to be abundant and also economical. About 85% of the world's energy is supplied by oil, coal and natural gas while nuclear, hydro, wind and solar power and biomass supply the rest. Coal, nuclear and hydro are used primarily to generate electricity while natural gas is widely used for heating. Biomass is used both for heating and cooking. The wind and solar power is the future's hope as they are sustainable energy sources. Oil powers almost all machines that move and that makes oil uniquely versatile. Oil powered airplanes carry 500 people across the widest oceans at nearly the speed of sound. Oil powered machines produce and transport food. Oil powered machines are ubiquitous. Clearly, we live in the age of oil but it is drawing to a close. According to data available if oil production remains constant until it's gone, there is enough to last 42 years. Oil wells will produce less as they become depleted, which will make it impossible to keep production constant. Similarly natural gas and coal will last another 61 years and 133 years respectively. Naturally, as they become scarce, they become expensive, leading to a worldwide energy crisis. If we are to survive on this planet, we have to make a transition to sustainable energy sources. The transition may be willy-nilly or planned - the choice is ours. The dawning era of limited and expensive energy will be very difficult for everyone on earth but will be even more difficult if it is not anticipated. It is of utmost importance that the public and policymakers understand the global energy crisis and act in tandem to ensure that the species 'homo sapiens' does not become extinct. The theme of the passage is