Problem 1. Consider the \"RLC\" circuit shown below. The circuit components have the values 80 = 5 v, R1 = 1 9,122 =0.1o,33 = 0.1 9,1. =0.001 H, and 0 = 0.001 F. (a) The switch 8 has been in Position 1 for a long time. What is the charge go on the capacitor? At time t = 0, the switch S is moved to Position 2. The rest of the problem is for this conguration of the circuit. Be sure to include the requested plots of q(t) vs. t and Hi) vs. t when you hand in your homework. (b) Using the equation for the charge g(t) on the capacitor given in Lecture 27 for the RLC circuit: q(t) = gas'9' cos aft (1) make a plot of q(t). Pick a good range of times (perhaps 0 S t g 0.1 s) so that you can see both the oscillations and the decay of q(t). Note on making plots in this assignment: if you are using a plotting program that plots a set of discrete points (e.g. Excel), it is important to make sure that you plot enough points per period of the oscillations to map out the oscillations clearly. If you don't see a nice decaying oscillation this is often the problem. ((3) Increase the value of R2 to 0.3 and replot (t). You should see the decay rate change. Give a brief physical explanation for this in terms of what is happening to the energy in the RLC circuit. ((1) Compute the analytic expression for the current I (t) in the circuit. (e) Make a plot of Ht) with R2 = 0.1 9.. While not required, if you can do it, it is instructive to graph t} on the same plot as q(t) from Part (b)J as this helps in illustrating the relationship between the two quantities