School of Mathematics and Statistics MAST10006 Calculus 2, Semester 1 2017, Assignment 4 Student Name Student Number Tutor's Name Tutorial Day/Time Submit your assignment to your tutor's MAST10006 assignment box before 4pm on Monday 15th May. This assignment is worth 5% of your final MAST10006 mark. Note: Full working must be shown in your solutions. Assignments must be neatly handwritten in blue or black pen. Diagrams can be drawn in pencil. Marks for individual questions are shown on the assignment. Marks will be deducted in every question for incomplete working, insufficient justification of steps and incorrect mathematical notation. 1. Find the general solution to the differential equation y 00 + 2y 0 + 3y = 1 + t2 + et . [12 marks] 2. Consider an electric circuit (see figure below) consisting of an inductor with an inductance of L = 0.5 Henry and a capacitor with a capacitance of C = 0.1 Farad connected in series with a voltage source of V (t) = 50 sin(t) Volts. L V (t) C (a) Show that the differential equation satisfied by the charge q(t) in this circuit is q + 20 q = 100 sin(t). (b) Determine the value(s) res for which resonance occurs. (c) Solve the initial value problem to find the charge qN R (t) as a function of time in the case where there IS NO resonance. (d) Solve the initial value problem to find the charge qR (t) as a function of time for one of the values res where there IS resonance (you can choose which res value to consider). [16 Marks]