Question

(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 1

To find the position of the ball below its rest position after t seconds in critically damped harmonic motion, we need to solve the equation of motion y = (A + Bt)e^(-bt) using the given initial conditions and constants A, B, and b.

Step-by-step explanation:

The problem describes the critically damped harmonic motion of a hollow steel ball suspended from a spring. The ball is started in motion with a downward velocity of 4 feet per second. The air resistance on the ball is numerically equal to 4 times its velocity. To find the position of the ball below its rest position after t seconds, we need to solve the equation of motion.

The equation of motion for critically damped harmonic motion is y = (A + Bt)e^(-bt), where A, B, and b are constants determined by the initial conditions. We can solve for these constants by plugging in the given initial conditions and solving the resulting system of equations. Once we have the values of A, B, and b, we can plug in the value of t to find the position y of the ball below its rest position.