A mass m moving in 1-d on a spring of force constant k experiences a damping force -bx in addition to a driving force of the form Fx = a(cos wt + sin wt) where a, b, w are positive, real constants. Using the complex notation as in our class notes, derive the steady-state motion of the mass, starting from Newton's second law, to show that x(t) = A cos(wt) and find A and o. (Hint: First express Fr as the real part of a complex expression.)