A space experimental package of mass \(m\) is supported on an elastic suspension of stiffness \(k\) in the space shuttle. During launching, the space shuttle (base of the elastically supported package) experiences an acceleration of \(\ddot{y}(t)=\alpha t\), where \(\alpha\) is a constant. Find the time variation of the displacement, \(x(t)\), and the relative displacement, \(x(t)-y(t)\), of the package. Assume zero initial conditions.