Question

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

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-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)...

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 ? (?)...

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, the system is immersed in a liquid that
offers 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 ? (?) at all...

A mass m is
attached to a spring with stiffness k=25 N/m. The mass is stretched
1 m to the left of the equilibrium point then released with initial
velocity 0.
Assume that m = 3 kg, the damping force is negligible,
and there is no external force. Find the position of the mass at
any time along with the frequency, amplitude, and phase angle of
the motion.
Suppose that the spring is immersed in a fluid with damping
constant...

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.

when a mass of 2 kg is attached to a spring whose constant is 32
N/m, it come to rest in the equilibrium position. at a starting
time t=0, an external force of y=80e^(-4t)*cos(4t) is applied to
the system. find the motion equation in the absence of damping.

When a mass of 4 kilograms is attached to a spring whose
constant is 64 N/m, it comes to rest in the equilibrium position.
Starting at t = 0, a force equal to f(t) = 80e−4t cos 4t is applied
to the system. Find the equation of motion in the absence of
damping.

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...

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 4 minutes ago

asked 5 minutes ago

asked 8 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 18 minutes ago

asked 25 minutes ago

asked 48 minutes ago

asked 52 minutes ago

asked 55 minutes ago

asked 1 hour ago