A 0.50kg mass is attached to a light horizontal spring of force constant k=200Nm−1. The mass is pulled 0.080m to the right of its equilibrium position and released from rest at t=0. Take the right direction as positive.
(i) Determine the amplitude, angular frequency, and phase constant of the subsequent motion.
(ii) Write the complete equations for displacement x(t), velocity v(t), and acceleration a(t).
(iii) Calculate x,v, and a at t=0.25s, giving each with its correct sign and unit.
(iv) Find the first instant after t=0 when the velocity of the mass becomes zero. State the corresponding displacement and acceleration at that instant.