Question

A mass weighing 16 pounds stretches a spring

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

the
instantaneous velocity. Find the equation of motion

8 |

3 |

1 |

2 |

x(t)

if
the mass is driven by an external force equal to
f(t) = 20 cos(3t).

(Use
g =
32 ft/s^{2}

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) = 10 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 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 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
sqrt(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 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.)

A mass of 1 slug, when attached to a spring, stretches it 2 feet
and then comes to rest in the equilibrium position. Starting at t =
0, an external force equal to f(t) = 4 sin(4t) is applied to the
system. Find the equation of motion if the surrounding medium
offers a damping force that is numerically equal to 8 times the
instantaneous velocity. (Use g = 32 ft/s2 for the
acceleration due to gravity.)
What is x(t) ?...

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
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 19.6 N stretches a spring 9.8 cm. The
mass is initially released from
a point 2/3 meter above the equilibrium position with a downward
velocity of 5
m/sec.
(a) Find the equation of motion.
(b)Assume that the entire spring-mass system is submerged in a
liquid that
imparts a damping force numerically equal to β (β > 0) times the
instantaneous
velocity.
Determine the value of β so that the subsequent motion is
overdamped.

A mass weighing 16 pounds is attached to a spring and stretches
it 4 feet. You release the mass from rest
one foot below equilibrium.
(a) What is the initial value problem that models this
scenario?
(b) What is the equation of motion?
(c) What is the period of motion?
(d) Assume now that there is a damping force equivalent to 6
times the velocity. Repeat parts (a) and (b).
(e) Now assume there is still the damping force, but...

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