Aforce of 4 pounds stretches a spring 1 foot. a mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity. (use g-32 ft/s2 for the acceleration due to gravity.) (a) find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) (b) express the equation of motion in the form x(t) = ae-at sin( v/ ? 2-12 t + e). (round ? to two decimal places.) x(c) (c) find the first time at which the mass passes through the equilibrium position heading upward

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons