Exercise 4 Consider the differential equation mit+ Km = 0 corresponding to a mass spring system where m is the mass, K is the spring constant and 1:06) is the position of the mass at time t. The solution with 3(0) = 0 is given by Assume that the mass m = 10, and the initial condition 33(0) > 0. The power spectrum of :z:(t) over the interval [0, n] is presented in the following gure. Find the initial condition arm) and the spring constant K. The power spectrum of |a k|2 vs k 1 I I I | r Figure 1: The power spectrum of $01) over the interval [0, 6w]