Problem 1

A mass

m

is attached to a light spring of stiffness

k

on a smooth horizontal surface, with the other end fixed. Let equilibrium be

x=0

, neglect spring mass and resistance, and release from rest at

x=A>0

. (a) Write the equation of motion and find the period. (b) Find maximum speed and its location. (c) Find speed as it passes

x=A/2

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.prevStep problems.proof.nextStep

x=A/2\Rightarrow v=\frac{\sqrt3}{2}A\sqrt{k/m}

problems.proof.analysis

Check against a limiting case, a stated condition, or an energy balance. A sound result must have the expected physical trend.