Type 1: Vibrating String with Zero Initial Velocity based Problem in Tamil Unit 3 Application of PDE

A string is stretched and fastened to two points x=0 and x=l apart. Motion is started by displacing the string into the form y = k(lx - x²) from which it is released at time t=0. Find the displacement of any point on the string at a distance of x from one end at time t.