Finding the Start-up Torque for a Shunt-wound Motor

I am having difficulty determining the start up torque for the motor. If you could also explain how to do the other parts that would be great. Thanks

Calculating Impedance and Current in a circuit

For the circuit attached, calculate the combined impedance of the 160 uh inductor and 10uf capacitor; and i(t) when Vs(t)=20 cos (wt+pi/4) V when w=25 Mrad/s in both instances. (Circuit is on attached file)

To find the inductor current in a switched circuit a long time after the switch is open.

A security alarm for an office building door is modeled by the circuit shown. The switch represents the door interlock, and V is the alarm indicator voltage. Find the current through the inductor, iL(t), for t>0. The switch has been closed for a long time at t=0. This was actually a problem posted by one of the students and I provided the solution. This is just a detailed solution (step-by-step) to the same problem.

The energy stored by a 1 mf capacitor.

Problem also in attached file. The energy stored by a 1 mf capacitor used in a laser power supply is given as W=4e(-10t) J for T>=0. what is the capacitor current at T=0.1s. A) -0.271 KA B) -0.271 A C) 0.271 A D) 1.472 A

Energy stored by a 1 mf capacitor. Find the capacitor voltage.

Problem also in attached file. The energy stored by a 1 mf capacitor used in a laser power supply is given as W=4e(-10t) J for T>=0. find the capacitor voltage at T=0.1 sec. A) 0.60V B) 1.5V C) 54.2V D) 89.4V