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Consider the system in the following diagram, where there is a viscous element B2, K1 is a translational element, and K2 is a rotational element. Let t(t) be the applied torque, x1 the displacement of M from rest, and u the angular displacement of the element J from rest (i.e., when the springs are neither stretched or compressed). The pulley has no inertia or friction, and the cable does not stretch.
(a) Write the differential equations that describe the system.
(b) Write the state variable equations that describe the system.
A vessel holding some liquid is placed in a vacuum chamber that is constantly pumped. Gas leaks from the vessel into the vacuum through a small hole, radius 4.15 micro m, but the pressure inside the vessel remains 38.6 kPa. After a day mass of the..
A paper by Ruckenstein and Tsai (1981)* shows that an "optimum pore size" can exist for catalytic reactions of large solute molecules in solvent-filled pores. Obtain the paper from your library and read it carefully. Then derive the analytical equati..
Assuming the total brush-contact drop to be 2 V, find the induced armature voltage at rated load and rated terminal voltage for
Steam at 100°C is passed into a condenser at a rate of 500 kg/h and leaves as water at 60°C. If the condenser is supplied with cooling water which enters at 20°C and leaves at 40°C, calculate:- how much heat per hour is extracted from the steam.
What is the kinetic energy and the potential energy of ball B at point II? The potential energy is given by PE mgz, where m is the mass in kilograms, g is the gravitational constant (9.81 m/s2), and z is the distance in meters.
If a wye-delta starting method is employed, find the starting current and the starting torque.
The feed (CAo= 1.0, CRo= 0, CSo= 0) enters two mixed reactors in series (?1= 2.5 min,?2= 10 min) knowing the composition in the first reactor (CA1= 0.4, CR1= 0.4, CS1= 0.2),find the composition leaving the second reactor (using fractional yield co..
A mixture of 65 mol% methane, 30 mol% hydrogen, and 5 mol% nitrogen is burned to heat a boiler used to produce hot steam. The ratio of CO2 to CO in the exhaust gas is 10:1. If 30% excess air is supplied, determine the concentration of the exhaust g..
Consider a 1-bit version of the digital comparator shown in Figure P6.1.41. Note that the operation of this circuit is such that whichever output is 1 gives the desired magnitude comparison.
Find the three highest speeds at which this linkage would be possible.
Find the slip at which the maximum developed torque occurs.
A sinusoidal signal, with amplitude of 3.25 volts, is applied to a uniform quantizer of the mid-tread type whose output takes on the values 0, ±1, ±2, ±3 volts. Sketch the waveform of the resulting quantizer output for one complete cycle of the in..
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