A block of mass m is connected to a spring of spring constant k as shown in Fig. The frame in which the block is placed is given an acceleration a towards left. Neglect friction between the block and the frame walls. The maximum velocity of the block relative to the frame is

Solve this question relative to the frame (car) of reference. For maximum velocity (relative to frame), the block must be in equilibrium position. Let x0 be the equilibrium elongation in spring, then ⇒ma = kx0 From work-energy theorem,mv22−0=−kx022+max0. This question is an application of using the work-energy theorem in non-inertial frame of reference.