Sample Problem : The spring-mounted slider moves in the horizontal guide with negligible friction and has a velocity v, 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 =-ks, where kis 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. S