\(\sum_{}^{}A_{n}sin(nk_{1}z); n = 1, 3, 5.....\) Formula 1 Formula 2 Prove the following two statements using a method that makes use of the normal modes of a continuous string with appropriate boundary conditions, and is equivalent to the the Fourier analysis of a periodic function of z. 1. Any reasonable function f(z) defined between z = 0 and z = L having a value of zero at z = 0 and slope zero at z = L can be expanded in a fourier series of the form as indicated in formula 12. Any reasonable function defined between z = 0 and z = L having zero slope at z = 0 and zero slope at z = L can be expanded as indicated in formula 2In case 1, k1L = pi/2, and k1L = pi in case 2