(b) A machine has a mass of 100 kg and unbalance reciprocating parts mass 2 kg...
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(b) A machine has a mass of 100 kg and unbalance reciprocating parts mass 2 kg which move through a vertical stroke of 80 mm with simple harmonic motion. The machine is mounted on four springs, symmetrically arranged with respect to centre of mass, in such a way that the machine has one degree of freedom and can undergo vertical displacements only. Case 1 Neglecting damping, calculate the combined stiffness of the spring in order that the force 1 of the applied force, when the speed of rotation of 25th transmitted to the foundation is machine crank shaft is 1,000 rpm. Case 2 When the system in free damped vibration, it is found that the amplitude of vibration after one complete vibration oscillation is 1 of the initial. With the condition of steady state 100 and resonance, determine the following. (i) The amplitude of steady state of vibration. (ii) The transmissibility of the system. (iii) The force transmitted to the foundation. Based on the results obtained give comments on the condition of steady state and resonance. (b) A machine has a mass of 100 kg and unbalance reciprocating parts mass 2 kg which move through a vertical stroke of 80 mm with simple harmonic motion. The machine is mounted on four springs, symmetrically arranged with respect to centre of mass, in such a way that the machine has one degree of freedom and can undergo vertical displacements only. Case 1 Neglecting damping, calculate the combined stiffness of the spring in order that the force 1 of the applied force, when the speed of rotation of 25th transmitted to the foundation is machine crank shaft is 1,000 rpm. Case 2 When the system in free damped vibration, it is found that the amplitude of vibration after one complete vibration oscillation is 1 of the initial. With the condition of steady state 100 and resonance, determine the following. (i) The amplitude of steady state of vibration. (ii) The transmissibility of the system. (iii) The force transmitted to the foundation. Based on the results obtained give comments on the condition of steady state and resonance.
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