A 50.0 g mass oscillating on a horizontal (massless) spring (k = 20 N/m) across a frictionless surface has an initial velocity of magnitude 50.0 cm/s to the left as it passes its equilibrium length. a) Defining the x-axis as pointing to the right, write the x-component of the velocity of the mass at t = 0 s. b) Draw a graph of v, versus time for this motion in terms of the period of the motion, T, and the amplitude of the motion, Vmax. Show two full periods, labelling every T/4. c) If the oscillation period israd, solve for the first time after t=0 s that the mass passes through equilibrium. Show all calculations, expressing your answer as a number with units. d) Solve for the amplitude of this oscillation. e) Sketch a graph of the position versus time of the oscillating mass, labelling T and A on your axes for two full periods. f) At t = T/4, what potential energy does the system have? Show all calculations. g) At t = 37/2, what kinetic energy does the system have? Show all calculations.