An ideal spring, with spring constant k, is attached to a particle of charge q and mass m in such a way that it can only move along the x-axis. The spring’s equilibrium is used to set x = 0. The system is then put in an electric field E~ = E ˆx. 1. Where would the new equilibrium be? 2. If the system was at rest and equilibrium initially, what is the maximum speed of the system after the electric field is turned on? 3. Under the same conditions what is the maximum distance from the origin the mass can reach?

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.