Question

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

x(t)= ?? m

Answer #1

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.

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.

a 3 kg mass is attached to a spring whose constant is 147 N/m,
comes to rest in the equilibrium position. Starting at t
= 0, a force equal to f (t) =
12e−5t cos 2t is applied to
the system. In the absence of damping,
(a)
find the position of the mass when t =
π.
(b)
what is the amplitude of vibrations after a very long
time?

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 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 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 spring with spring constant 4 N/m is attached to a 1kg mass
and a dashpot with damping constant 4 Ns/m.A periodic force equal
to 2 cos(t) N is applied to this system. Assume that the system
starts withx(0) = 1 andx′(0) = 2,

A body of mass equal to 4 kg is attached to a spring of constant
k = 64 N / m. If an external force F (t) = 3/2 cos 4t is applied to
the system, determine the position and speed of the body at all
times; suppose that the mass was in position x (0) = 0.3 m and, at
rest, at time t = 0 s

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)...

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