For the transverse vibration of a simply supported uniform beam, solve for the transient response if the initial conditions are given by

\[ y(x, 0)=B\left(\frac{x}{L}-3 \frac{x^{2}}{L^{2}}+2 \frac{x^{3}}{L^{3}}\right) \quad \dot{y}(x, 0)=0 \]