A 0.40kg glider is attached to an ideal horizontal spring and oscillates without friction. The angular frequency of the motion is 6.0rads−1. At t=0s the glider is 0.030m to the right of equilibrium and is moving leftward with a speed equal to exactly one-half of its maximum speed during the oscillation.
(a) Derive a numerical value for the phase angle φ (in radians, between 0 and 2π) that satisfies the stated initial conditions.
(b) Using your value of φ, determine the amplitude A of the oscillation.
(c) Write the analytical expression for the displacement x(t) that models the glider’s motion.
(d) Calculate the time, measured from t=0s, at which the glider first reaches its maximum leftward displacement. Explain each step in your reasoning.