[10] (5) A certain guitar string (linear density ,2: = 1.5 gm, length L = 60 cm and tension F r = 160 N} is plucked at time t = U at U4 of one of its fixed ends [as shown in Figure]. The string is displaced a distance d = 0.5 cm. [4] (3a) Reproduce the initial triangular shape at t = U i. e., the function f(x,0) by adding together the normal modes {Fourier Components) of the string with appropriate amplitudes (Fourier Amplitudes). Find the numerical values of the first two amplitudes for this function. [2] (5b) Find the numerical values of the first two angular frequencies of the string. [4] (5c) Write clots-\"n mathematical expression for the shape of the string (i.e., y as a funcuon of X) one second after plucking the string (utilizing the numerical values _vou found in 5.a and 5.13)