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(a) Obtain the transfer function
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- Find the transfer function, G(s)=θ2(s)/T(s), for the rotational mechanical system with gears. Determine the two equations of motion.arrow_forwardFor the system shown in figure below, derive the differential equation of motion for small oscillation. If m1=m2=1 kg, k1=k2=1000 N/m, c1=c2=10N·s/m, a=b=0.5 m, and l=1 m find the solution after 1 s provided that the initial angular displacement is zero and the initial angular velocity is 5 rad/s. Assume that the rod is massless.arrow_forwardDetermine the natural frequency of the system shown beside using Motion equationarrow_forward
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- A spring is stretched 200 mm by a 15-kg block. If the block is displaced 200 mm downward from its equilibrium position and given a downward velocity of 0.75 m/s, What is the phase angle? Assume that positive displacement is downward.arrow_forwardIn the system shown in Figure 1, assume that the rod pivoted at point P is massless and perfectly rigid. A mass m is attached to the other end of the rod and supported by a damper at distance L, and a spring at a distance L2 to the pivot point P. The displacement x of the mass is measured from the equilibrium position of the system. Assuming that x is small, obtain the equation of motion of the system by applying Newton's laws.arrow_forwardGiven the following mechanical system, determine the transfer function G (S) = (X_2 (S)) / (F (S))arrow_forward
- A reciprocating compressor of mass 20 Kg runs at a constant speed of 3000 rpm. After installation the forcing frequency is found to be too closer to the natural frequency of the system. Design a dynamic vibration absorber such that (a) the natural frequency of the main system is equal to that of the absorber and (b) the ratio of the operating frequency to the natural frequency is 0.75.arrow_forwardFor the rotational system shown in the figure, write the equations of motion from which the transfer function, G(s) = θ1(s)/T(s), can be found.arrow_forwardA 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equations of motion if the following is true. (Show a sketch of the problem) (a) the mass is initially released from rest from a point 1 meter below the equilibrium position (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s (c) In parts a and b of the problem, determine whether the mass passes through the equilibrium position. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?arrow_forward
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