Problem 1
A mass is attached to a light spring of stiffness on a smooth horizontal surface, with the other end fixed. Let equilibrium be , neglect spring mass and resistance, and release from rest at . (a) Write the equation of motion and find the period. (b) Find maximum speed and its location. (c) Find speed as it passes toward equilibrium. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.
problems.proof.stepOf
problems.proof.analysis
Apply the governing law for the stated model, using the sign convention in the problem. This provides the starting equation for the later parts.
problems.proof.pitfall. Maximum speed occurs at equilibrium, not at the turning point where the mass is released from rest.