Consider a capacitor made of two very large perpendicular plates. (Let the positive
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- Two tanks are connected as in Figure 1.6. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into tank 2 at the rate of 5 gallons per minute, and tank 2 also has an output of 5 gallons per minute. Deter- mine the amount of salt in each tank at any time. Also, determine when the concentration of salt in tank 2 is a minimum and how much salt is in the tank at that time. Hint: Solve for the amount of salt in tank 1 at time t and use this solution to help determine the amount in tank 2. 5 gal/min: 1/2 Ib'gal 5 gal'min Tank 1 Tank 2 5 gal'minarrow_forward2. A platform edge x(1) section of a uniform chain of length 8 ft is loosely wound around a peg at the edge of a high horizontal platform, and the remaining part of the chain hangs still on the edge of the platform. The length of the extended chain is 3 ft, the chain weighs 2 Ib/ft, and the positive direction is downwards. Starting at t = 0 seconds, the weight of the outstretched part causes the chain on the table to slip smoothly and fall to the floor. If x(t) represents the length of the chain protruding into the table at time t = 0, then v = dx/dt is the velocity. When all resistive forces are neglected, it can be shown that the mathematical model relating v to x is: dv XV-+ v2 = 32x dxarrow_forwardConsider the forced damped oscillator equation y'' +9y = F sin(wt) For this forced oscillator to exhibit resonance, w =arrow_forward
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