A railway wagon, moving with velocity v, strikes a viscously damped buffer. The motion of the wagon can be represented by the following differential equation: V(0) = V where m 5,000 kg is the mass of the wagon, c = 15,000 N-s/m is the damping coefficient, and the initial velocity (at / 0) is vo- 3 m/s. The analytical solution of this initial value problem is: v(t) = 3e" ) One approach for solving this problem numerically is using the Euler's method, where the first derivative is approximated by the finite difference equation: At Substituting the derivative in the ode yields the following iterative equation: *1 = 11 - a) Write a MATLAB script for solving the differential equation using the Euler's method, from 1 0 to 2 seconds, using a step size of At = 0.1 s. b) Plot the results obtained in parts (a) together with the true solution. Include axis titles, plot title, gridlines and legend. A hollow, conducting sphere with an outer radius of 0.260 m and an inner radius of 0.200 m has a uniform surface charge density of +6.27 x 10-6 C/m. A charge of -0.700 C is now introduced into the cavity inside the sphere. Part A What is the new charge density on the outside of the sphere? Express your answer with the appropriate units