(1 pt) this problem is an example of critically damped harmonic motion. a hollow steel ball weighing 4 pounds is suspended from a spring. this stretches the spring 18 feet. the ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. the air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . suppose that after t seconds the ball is y feet below its rest position. find y in terms of t. take as the gravitational acceleration 32 feet per second per second. (note that the positive y direction is down in this problem.) y=
Answer:
Hooke's Law along with Newtons second Law of motion.
x"+(a/m)x'+(k/m)x=F(t)/m
x"+(256)x'+(96)x=0
F=-kx
F=-4
x=1/3
mg=4
m=4/32
m=1/8
-4=-k* (1/3)
k=12
x"+(256)x'+(96)x=0
y=C1e^(4*(1018)^(1/2)-128)*t+C2e^(-4*(...
