Find the free vibratory response of an undamped single-degree-of-freedom system with \(m=1\) and \(k=1\), using the central difference method. Assume \(x_{0}=0\) and \(\dot{x}_{0}=1\). Compare the results obtained with \(\Delta t=1\) and \(\Delta t=0.5\) with the exact solution \(x(t)=\sin t\).