Question

A mass weighing 16 pounds stretches a spring 1 feet. It is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s. Find the equation of motion. Determine the amplitude, period, and frequency of motion. (Use g = 32 ft/s2 for the acceleration due to gravity.)

Answer #1

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/s^2 for the acceleration due to...

A mass weighing 20 pounds stretches a spring 6 inches. The mass
is initially released from rest from a point 4 inches below the
equilibrium position.
(a) Find the position x of the mass at the times t = π/12, π/8,
π/6, π/4, and 9π/32 s. (Use g = 32 ft/s2 for the acceleration due
to gravity.)

A 4-foot spring measures 8 feet long after a mass weighing 8
pounds is attached to it. The medium through which the mass moves
offers a damping force numerically equal to
2
times the instantaneous velocity. Find the equation of motion if
the mass is initially released from the equilibrium position with a
downward velocity of 9 ft/s. (Use
g = 32 ft/s2
for the acceleration due to gravity.)
x(t) =
Find the time at which the mass attains its...

A mass weighing 20 N stretches a spring 6 m. The mass
is initially released from rest from a point 8 m below
the equilibrium position.
(a) Find the position x of the mass
at the times
t = π/12, π/8, π/6, π/4, and
9π/32 s.
(Use
g = 9.8 m/s2
for the acceleration due to gravity.)

a
mass weighing 24 pounds, attached to the end of a spring, stretches
it 4 inches. initially, the mass is released from rest from a point
of 2 inches above the equilibrium position. find the equation of
motion. (g= 32 ft/s^2)

A mass weighing 10 lb stretches a spring 1/4 foot. This mass is
removed and replaced with a mass of 1.6 slugs, which is initially
released from a point 1/3 foot above the equilibrium position with
a downward velocity of 3/4 ft/s. Find the first time the mass will
be positioned half of the amplitude below the equilibrium.

A force of 64 pounds stretches a spring 4 feet. A mass of 4
slugs is attached to the spring and is initially released from rest
2 feet below the equilibrium position. (a) Suppose the spring has a
damping force equal to 16 times the instantaneous velocity and is
being driven by an external force, ?(?) = 4 cos(5?) . Write the IVP
that this problem describes. (3 pts) (b) Solve the equation in part
(a) to obtain the equation...

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....

1. A 4 pound weight stretches a spring 6
inches. The mass is then released from an initial position of 4
feet below the equilibrium position with an initial upward velocity
of 24ft/s.
(a) What is the frequency of motion?
(b) Determine the first time the mass crosses the
equilibrium position. Round to 3 decimals places.
(c) Determine the first time the mass attains its
extreme displacement from the equilibrium position. Round to 3
decimal places.

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