Obtain the differential equation governing the motion of the one degree of freedom system shown in Fig. Below. Also determine the undamped natural frequency of the system.

An array of m-50 thermoelectric modules is installed on the exhaust of a sports car. each module has an effective seebeck coefficient of sp of 0.143 5vk and an internal electrical resistance of r.-4 ? in addition, : (15 points each module is of width w 60mm and contains n=100 pairs of semiconducting pellets. each pellet hasan overall length of 2l-5mm and a cross-sectional area as 1.2 x 10'm and is characterized by a thermal conductivity of kpl2w rnk. the hot side of each module is exposed to exhaust gases at·p650c with hia4ow rrk while the osite side of each module is cooled by pressurized water at surface) and 156 °c (at the cool surface). 11s c with h: -500w/m'k. the modules are wired n series and the load resistance is r d=400ohm .the module surface temperatures, t, and ts are 183 "c (at the hot surface and 156c (at the cool surface) a)-draw a schematic of this scenario and label all parts. a. b. if the induced current, i, is 0.15 amps, what is the total power (pa) for one module? c. what is the total power harvest from the exhaust with all 50 modules?

Steam enters a turbine at steady state at 2 mpa, 360°c with a velocity of 100 m/s. saturated vapor exits at 0.1 mpa and a velocity of 50 m/s. the elevation of the inlet is 3 m higher than at the exit. the mass flow rate of the steam is 15 kg/s, and the power developed is 7 mw. let g 9.81 m/s^2. determine: a)-the area at the inlet, in m^2 b)-the rate of heat transfer between the turbine and surroundings, in kw c)-draw a p-v diagram for this process.

An electric cable of 10 mm in diameter is to laid in atmosphere at 20°c. the estimated surface temperature of the cable due to heat generation is 65°c. find out ther maximum percentage, increese in heat dissipated when the wire is insulated with rubber having k =0155 w/m-k. take h=8.5w/m^2.k