Question

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 1/2 feet. The ball is started in motion from the equilibrium position with a downward velocity of 6 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. (Note that the positive direction is down.)

Take as the gravitational acceleration 32 feet per second per
second.

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Answer #1

A hollow steel ball weighing 4 pounds is suspended from a
spring. This stretches the spring 12 feet. The ball is started in
motion from the equilibrium position with a downward velocity of 8
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. (Note that the...

A hollow steel ball weighing 4 pounds is suspended from a
spring. This stretches the spring 13 1 3 feet. The ball is started
in motion from the equilibrium position with a downward velocity of
7 7 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....

A hollow steel ball weighing 4 pounds is suspended from a
spring. This stretches the spring \frac{1}{6} feet. The ball is
started in motion from the equilibrium position with a downward
velocity of 3 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. (Note that the...

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 1818 feet. The ball is started in
motion from the equilibrium position with a downward velocity of 55
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...

A steel ball weighing 128 lb is suspended from a spring,
whereupon the spring is stretched 2 ft from its natural length. The
ball is started in motion with no initial velocity by displacing it
6 in above the equilibrium position. Assuming no air resistance,
find (a) an expression for the position of the ball at any time t,
and (b) the position of the ball at t = π 12 sec.
Please show all the work on paper and...

A
mass weighing 8 pounds stretches a spring 2 feet. At t=0 the mass
is released from a point 2 feet above the equilibrium position with
a downward velocity of 4 (ft/s), determine the motion of the
mass.

A mass weighing 24 pounds attached to the end of the spring and
stretches it 4 inches. The mass is initially released from rest
from a point 3 inches above the equilibrium position with a
downward velocity of 2 ft/sec.
Find the equation of the motion?

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 3 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1/2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 10 cos(3t).
(Use g = 32 ft/s^2 for the acceleration due to...

A mass weighing 16 pounds stretches a spring
8
3
feet.
The mass is initially released from rest from a point
3 feet
below the equilibrium position, and the subsequent motion takes
place in a medium that offers a damping force that is numerically
equal to
1
2
the
instantaneous velocity. Find the equation of motion
x(t)
if
the mass is driven by an external force equal to
f(t) = 20 cos(3t).
(Use
g =
32 ft/s2
for
the acceleration...

A mass weighing 16 pounds stretches a spring 8 3 feet. The mass
is initially released from rest from a point 3 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1 2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 10 cos(3t).
(Use g = 32 ft/s2 for the acceleration...

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