Physic Labs

Problem 1

A mass mm is attached to a light spring of stiffness kk on a smooth horizontal surface, with the other end fixed. Let equilibrium be x=0x=0, neglect spring mass and resistance, and release from rest at x=A>0x=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/2x=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.
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vmax=Ak/mv_{max}=A\sqrt{k/m}
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Use the result just found to calculate the quantity requested next. Keep the sign convention consistent throughout.