Question 16.19: A tightly stretched flexible string has its ends fixed at x ...
A tightly stretched flexible string has its ends fixed at x = 0 and x = 1. The string is plucked at middle point by an initial displacement 0.05 and then released from this position. Find the transverse displacement of a point at a distance x from one end and at any time t of the vibrating string. The displacement at any time t and at a distance x satisfies the wave equation \frac{\partial^2 u}{\partial t^2}=4 \frac{\partial^2 u}{\partial x^2} .
Take the step size for t is 0.1 and step size for x is 0.25. Use explicit scheme to compute the solution up to time t = 0.3. Use central difference formula for the derivative term in the initial condition.
The mathematical model for this problem is exactly same as in Example 16.18. So, the solution to this problem is the solution of Example 16.18.