1. An electric circuit contains a resistance R and a capacitor C in series, and a...

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1. An electric circuit contains a resistance R and a capacitor C in series, and a battery supplying a time-varying electromotive force V(t). The charge q on the capacitor therefore obeys the equation bp dt R V (t) Assume that initially there is no charge on the capacitor, and given that V(t) = Vo sin(t) (a) Find the Integrating Factor for the above equation. (b) Solve the differential equation. Hint: You might find using q(0) = 0 useful. 2. The study of sawtooth waves in electrical engineering leads to integrals of the form tsin(Kwt) dt where K is an integral and w is a nonzero constant. Evaluate the integral. 1. An electric circuit contains a resistance R and a capacitor C in series, and a battery supplying a time-varying electromotive force V(t). The charge q on the capacitor therefore obeys the equation bp dt R V (t) Assume that initially there is no charge on the capacitor, and given that V(t) = Vo sin(t) (a) Find the Integrating Factor for the above equation. (b) Solve the differential equation. Hint: You might find using q(0) = 0 useful. 2. The study of sawtooth waves in electrical engineering leads to integrals of the form tsin(Kwt) dt where K is an integral and w is a nonzero constant. Evaluate the integral.