The spring-mounted slider moves in the horizontal guide with negligible friction and has a velocity \(v_{0}\) in the \(s\)-direction as it crosses the mid-position where \(s=0\) and \(t=0\). The two springs together exert a retarding force to the motion of the slider, which gives it an acceleration proportional to the displacement but oppositely directed and equal to \(a=-k^{2} s\), where \(k\) is constant. (The constant is arbitrarily squared for later convenience in the form of the expressions.) Determine the expressions for the displacement \(s\) and velocity \(v\) as functions of the time \(t\).

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y, m t=0 100 60 80 60 40 20 1 2 4 3 0. -55 0 20 40 A 60 80 x, m Path Path =-30 m/s a = -16 m/s3 A 0 53.1% Ya, -8 m/s2 v = 50 m/s = a = 17.89 m/s Yu, -40 m/s (y)