Problem 2: Charging of a capacitor In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V₁, R₁, R₂, and C. (a) We first consider what happens att → ∞. What is the current in the capacitor? What is the po- tential difference on R₂ and the charge on the capacitor, Q? (b) Now for t > 0, derive the differential equation governing the time evolution of the capacitor's charge Q(t). (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. R₁ C R₂ www

Q1 The moment equation for a triangular distributed load, wo 30 N/m acted on a beam (Figur Q1) with a length, L- 5 m is given as: M₂-5x³-112.5x + 125 By performing your calculation in 3 decimal points: Determine the most positive roots of the system, x by using Newton Rhapson Method. Use initial value of x = 3. Iterate until |E <0.25). (b) Determine the most positive roots of the system, x by using Secant Method. Use initial value of x= [3,5]. Iterate until E<0.25).

where a 0, to find the a and B, such that y = ax + B. Your answers should be expressed in terms of a and b. α Eliminate the parameter t from the set of parametric equations. x = at + b y = 2t - 1 В