Answer to Question #338367 in Mechanical Engineering for Ammar

Question

find response (deflection) y (x,t) of The Vibrating string Length (L=𝜋), end fixed

c²=1 if The initial displacement and Initial Velocity are:

y (x,0) = o , 𝑦'(x,0) =0.1 Sin2x.

y (x,0) = o , 𝑦'(x,0) =0.01x , if 0 ≤ 𝑥 ≤𝜋/2

𝑦'(x,0) =0.01(𝜋 -x) , if 𝜋/2≤ 𝑥 ≤ 𝜋

y (x,0) = 0.1 Sinx , 𝑦'(x,0) = - 0.25 Sinx.