Assume the system in problem 2. below is being excited by pure white noise (random excitation). solve the problem via fourier transforms (equations 12.44 and 12.45 in your textbook). take the fourier transform of the equation. the fourier transform of white noise is constant in the frequency domain. after solving for x(f), take the inverse fourier transform to obtain x(t). this solution is equivalent to another type of solution covered in the course. 2. a vibrating system has the following constants: w=40.6 lb, k=50lb/in., and c=0.40 lb/in. per sec. determine a) the damping factor, b) the natural frequency of damped oscillation, c) derive the frequency response function (frf) and plot it as a bode plot (matlab or excel) d) find the half power bandwidth, predict damping factor via the half power bandwidth.