Question

A 1-kg mass is attached to a spring whose constant is 16 N/m and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equation if (A) The weight is released 60 cm below the equilibrium position. x(t)= ; (B) The weight is released 60 cm below the equilibrium position with an upward velocity of 17 m/s. x(t)= ; Using the equation from part b, (C) Find the time when the weight is at maximum displacement above equilibrium: t= ; (D) Find the maximum displacement above equilibrium in centimeters (cm):

Answer #1

A 1-kilogram mass is attached to a spring whose constant is 18
N/m, and the entire system is then submerged in a liquid that
imparts a damping force numerically equal to 11 times the
instantaneous velocity. Determine the equations of motion if the
following is true.
(a) the mass is initially released from rest from a point 1
meter below the equilibrium position
x(t) = m
(b) the mass is initially released from a point 1 meter below
the equilibrium...

A 1-kilogram mass is attached to a spring whose constant is 16 N
/ m, and then the entire system is immersed in a liquid that
imparts a damping force equal to 10 times the instantaneous speed.
Determine the equations of motion if the mass is initially released
from a point 1 meter below the equilibrium position.
differential equations

A mass of 4 Kg attached to a spring whose constant is 20 N / m
is in equilibrium position. From t = 0 an external force, f (t) =
et sin t, is applied to the system. Find the equation of motion if
the mass moves in a medium that offers a resistance numerically
equal to 8 times the instantaneous velocity. Draw the graph of the
equation of movement in the interval.

A force of 400N stretches a string 2 meters. A mass of 50kg is
attached to the end of the spring and stretches the spring to a
length of 4 meters. The medium the spring passes through creates a
damping force numerically equal to half the instantaneous velocity.
If the spring is initially released from equilibrium with upward
velocity of 10 m/s.
a) Find the equation of motion.
b) Find the time at which the mass attains its
extreme displacement...

A mass weighing 4 pounds is attached to a spring whose constant
is 2 lb/ft. The medium offers a damping force that is numerically
equal to the instantaneous velocity. The mass is initially released
from a point 1 foot above the equilibrium position with a downward
velocity of 12 ft/s. Determine the time at which the mass passes
through the equilibrium position. (Use g = 32 ft/s2 for the
acceleration due to gravity.)
s
Find the time after the mass...

MASS SPRING SYSTEMS problem (Differential Equations)
A mass weighing 6 pounds, attached to the end of a spring,
stretches it 6 inches.
If the weight is released from rest at a point 4 inches below
the equilibrium position, and the entire system is immersed in a
liquid that imparts a damping force numerically equal to 3 times
the instantaneous velocity, solve:
a. Deduce the differential equation that models the mass-spring
system.
b. Calculate the displacements of the mass ? (?)...

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 4 kg mass is attached to a spring with stiffness 48 N/m. The
damping constant for the spring is 16\sqrt{3} N - sec/m. If the mas
is pulled 30 cm to the right of equilibrium and given an initial
rightward velocity of 3 m/sec, what is the maximum displacement
from equilibrium that it will attain?

When a mass of 3 kilograms is attached to a spring whose
constant is 48 N/m, it comes to rest in the equilibrium position.
Starting at t = 0, a force equal to
f(t) =
51e−2t cos
4t is applied to the system. Find the
equation of motion in the absence of damping.
x(t)= ?? m

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