Laplace Transforms · Challenge problem

Two equal masses joined by springs satisfy $x'' = -10x + 6y$ and $y'' = 6x - 10y$. They start at rest with $x(0) = 1$, $y(0) = 0$, $x'(0) = y'(0) = 0$. Use the Laplace transform to find $y\!\left(\dfrac{\pi}{6}\right)$.