Solve for the string response, Equation 7.27, given the following initial conditions:

(a) \(y(x, 0)=0, \dot{y}(x, 0)=g(x)\)
(b) \(y(x, 0)=\sin \pi x / L, \dot{y}(x, 0)=0\)
(c) \(y(x, 0)=0, \dot{y}(x, 0)=\sin \pi x / L\)
(d) \(y(x, 0)=\sin \pi x / L, \dot{y}(x, 0)=\sin \pi x / L\).

In all cases, sketch the initial conditions and plot the response \(y(x, t)\).

2 TTC y(x,t) = sin A, sin mL L r=1 + B, cos TTC ), L (7.27)