Reference no: EM132492198

Question 1: Obtain the transfer function V_o(s)/V₁N(s) for the op-amp system shown below.

Question 2: For the RLC circuit shown below:

a) Obtain the transfer function, V₀(s)/V_s(s)

b) Obtain the equation of motion (ODE): v_o(t) in terms of v_a(t)
c) Determine the natural frequency
d) Determine the damping ratio

Question 3: For the RLC circuit shown below:

a) Obtain the transfer function, V₀(s)/V_s(s)

b) Use the transfer function to obtain the equation of motion: v_o(t) in terms of v_s(t)

Question 4 An large egg taken from a refrigerator (at 2°C) and dropped into a pot of boiling water takes approximately 12 minutes (or 720 seconds) to become hard-boiled. Assume that a hard boiled egg has effectively reached the same temperature as the boiling water (100 °C).

If a large egg has a mass of 0.07 kg, and a specific heat of 1000 Watt-sec./kg-°C, what is the thermal resistance between the water and the egg? You must show your work for full credit.

Question 5: Consider an armature-controlled DC motor. The physical model is shown below.

The motor parameters are:
I = 0.00012 Kg.m² R_a = 11.2 Ω v_a= 30V L_a≈0
a) The stall torque was measured to be 0.10 N-meters. Determine the values of K_T and K_b.
b) The no-load speed was measured to be 3500 rpm, determine the value of the torsional damping factor (c).
c) Determine the time constant.
d) Sketch a nicely labeled graph of no-load speed (rpm) vs time, for this motor, with a step input of 30 V.

Question 6 : Consider the thermal system shown in the figure below. It is comprised of a metal container with an electrical heater embedded in the bottom (a hot-pot), liquid inside the container, and air surrounding the pot and the liquid.

Assume that there is convection heat transfer between the pot and the liquid (h1, Al), convection heat transfer between the pot and the air (h2, A2) and convection heat transfer between the liquid surface and the air (h3, A3). You may assume: constant air temperature (To), lumped temperature for the pot (To) and lumped temperature for the liquid (Ti.)- You may assume that all other geometry (such as volume of the liquid and pot, etc) and all other properties (such as specific heats, heater voltage and resistance) are known.
a) Obtain the equation of motiion (ODE) for the temperature of the liquid.
b) Obtain the equation of motiion (ODE) for the temperature of the pot.
c) At steady state, which element will be hottest (air, liquid or pot)? Explain your answer.

Question 7: Consider the combined fluid-mechanical system shown below. The fluid is compressible, but the fluid inertance, the friction in the piston and the mass of the piston are negligible. When P₁ = P_atm, there is no force in the spring, the piston is located a distance xo from the right hand wall, and x = 0.

For the follwing questions, assume that all necessary fluid properties and geometry measurements are known. Use reasonable symbols for those items such as A, for the area of the piston in tank 1, V2 for the volume of tank 2 etc.

a) Write all of the equations that are true, regardless of whether the fluid is a liquid or a gas (equations that are true for both). Label those equation with words describing the physical principle used in the equation (ex. Conservation of mass, flow resistance, etc)
b) Write any additional equations that are true if the fluid is a liquid:
c) Write any additional equations that are true if the fluid is a fin:

Question 8: Consider the fluid-mechanical system shown below. The fluid in the tank is compressible but has no inertance or resistance. The line has only linear-resistance and inertance. The tank pressure is Pi and the tank volume is Vi. The system input is the supply pressure, Ps .

For the follwing questions, assume that all necessary fluid properties and geometry measurements are known. Use reasonable symbols for those items such as AL for the area of the line, L for the length of the line, etc.

a) Draw an equivalent electric circuit diagram for this system. Because we must use a lumped parameter assumption for the line, assume that the resistance comes first.

b) Write all of the equations that are true, assuming that the fluid is a liquid. Label those equation with words describing the physical principle used in the equation (ex. Conservation of mass, flow resistance, etc)