a) b) ww R 45) с I(t) C 00000 Consider a circuit consisting current source connected directly to a capacitor as shown above in (a). Its driving point impedance as seen from the source is Z(s), where the capacitance C = 0.018 F. (a) Suppose the current source varies with time according to I,(t) = 0.001 sin 5.31. i. What is the magnitude of the impedance at that frequency? ii. What is ve(t), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). (b) Suppose the current source is instead constant, given by I,(t)=0.005 Amps. i. What is the magnitude of the impedance at that frequency? ii. What is ve(), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). Note: you may want to solve this using the differential equation directly. (c) Now suppose an inductor with inductance L and a resistor of resistance R are added to the circuit, so that the inductor is in parallel with the capacitor, and both are connected in series with the resistor as shown above in (b). What is the driving point impedance of this new circuit as seen from the current source? For simplicity, please use the symbol C in your answer, rather than its numerical value.

consider a crane with a 30 pound ball suspended from a 40 foot cable that weighs 5 pounds per foot.a) find the work required to wind up 15 feet of hte apparatus.b) find the work required to wind up all 40 feet of the apparatus.

A new type of energy absorber is being designed as a buffer at the end of track at a fairground.It consists of a piston with small holes that moves in a cylinder containing oil, so that the kineticenergy of impact is absorbed as heat by the oil.a) Draw a sketch for the instant of impact by a vehicle of mass 2500kg moving at 30mphshowing the forces and energy transfers involved.b) Write down the first law of thermodynamics for a system and identify terms that are notrelevant if the oil is taken as the system.c) How much heat transfer to the surroundings is required to return the oil to its originaltemperature after an impact by a 2500kg vehicle moving at 30mph?

4.) Please help with equation, gravity is g=32.2 ft/sec^2 or g=9.81 m/sec^2