A mass weighing 8 pounds is attached to a spring. Whenset in motion, the spring/mass system exhibits simpleharmonic motion. Determine the equation of motion ifthe spring constant is 1 lb/ft and the mass is initiallyreleased from a point 6 inches below the equilibriumposition with a downward velocity of . Express theequation of motion in the form given in (6).

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.