Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_253

3/253 The block of mass \( m \) is attached to the frame by the spring of stiffness \( k \) and moves horizontally with negligible friction within the frame. The frame and block are initially at rest with \( x = x_0 \), the uncompressed length of the spring. If the frame is given a constant acceleration \( a_0 \), determine the maximum velocity \( \dot{x}_{max} = (v_{rel})_{max} \) of the block relative to the frame.