A small bead of mass m, carrying a charge q, is constrained to slide along a thin rod of length L. Charges Q are fixed at each end of the rod. a) Obtain an expression for the electric field due to the charges Q as a function of x, where x is the distance from the midpoint of the rod. (Answer is kQ[(L/2+x)^-2 - (L/2-x)^-2]^I) b) Show that for x << L, the magnitude of the field is proportional to x. c) Show that if q is of the same sign as Q as, the force that acts on the object mass m is always directed toward the center of the rod and is proportional to x. d) Find the period of the oscillation of the mass m if it is displaced by a small distance from the center of the rod and then released. (Answer is 2 * pi * sqrt(mL^3 /32kqQ) ). -------------------- So part (a) was pretty easy. I just did E = kQ/r^2 – kQ/r^2 and got the book answer. The next three parts i don't know what to do. For part (d) i know that T = 2 pi * sqrt(m / k). Then i did kx = qE to solve for "k" of spring, plugged in E, but it left me with some overly complicated equation. Anyways, thanks for any help in advance.