Question
In: Physics
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and...
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and the entire system is then submerged in a liquid that imparts a damping force equal to 8 times the instantaneous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force f(t) = 2U(t−1)*e^(−2(t−1)) is applied.
(a) Write f(t), the external force, as a piecewise function and
sketch its graph.
(b) Write the initial-value problem.
(c) Solve the initial-value problem.
(d) What type of motion does the solution of the initial value
problem describe? (forced undamped motion, forced overdamped
motion, forced critically damped motion, or forced underdamped
(oscillatory) motion)
Solutions
genius_generous answered 2 years agoRelated Solutions
A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire...
A 1-kilogram 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. The mass is initially released from rest
from a point 1 meter below the equilibrium position.
1. Show the Diagram, given and required only
( No need to solve, Thumbs up will only be given if 1 is
followed.)
A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...
A mass weighing 4 N is attached to a spring whose constant is 2
N/m. The medium offers a damping force that is numerically equal to
the instantaneous velocity. The mass is initially released from a
point 1 m above the equilibrium position with a downward velocity
of 6 m/s. Determine the time at which the mass passes through the
equilibrium position. (Use
g = 9.8 m/s2
for the acceleration due to gravity.)
14
s
Find the time after the...
A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...
A mass weighing 4 N is attached to a spring whose constant is 2
N/m. The medium offers a damping force that is numerically equal to
the instantaneous velocity. The mass is initially released from a
point 1 m above the equilibrium position with a downward velocity
of 6 m/s. Determine the time at which the mass passes through the
equilibrium position. (Use
g = 9.8 m/s2
for the acceleration due to gravity.)
s
Find the time after the mass...
A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to...
A vertical spring (ignore its mass), whose spring constant is
825 N/m , is attached to a table and is compressed down by 0.160
m.
A)What upward speed can it give to a 0.360-kg ball when
released? Express your answer to three significant figures and
include the appropriate units.
B) How high above its original position (spring compressed) will
the ball fly? Express your answer to three significant figures and
include the appropriate units.
a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...
a block of mass m=0.10 kg attached to a spring whose spring
constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and
the velocity v=-2.0m/s
a) find the equation of displacement as a function of time
b) sketch the displacement as a function of time for the first
cycle starting t=0s
When a 5 kg mass is attached to a spring whose constant is 180 N/m, it...
When a 5 kg mass is attached to a spring whose constant is
180 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
20e−3t cos 6t 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
When a 6 kg mass is attached to a spring whose constant is 24 N/m, it...
When a 6 kg mass is attached to a spring whose constant is
24 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
42e−7t cos 4t 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?
When a 6 kg mass is attached to a spring whose constant is 294 N/m, it...
When a 6 kg mass is attached to a spring whose constant is
294 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
12e−4t cos 3t 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?
1. A 1 kilogram mass is attached to a spring with a spring constant of 4...
1. A 1 kilogram mass is attached to a spring with a spring
constant of 4 N/m. Write the equation of motion if the spring is
stretched 25 cm below the equilibrium position and released.
a) Suppose the system experiences a constant forcing function
downwards of 4 N. (Note that one would need to divide by the mass,
but the mass is 1 kg so we don’t see a difference here.) Solve the
non-homogeneous equation. (Keep everything else about the...
A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...
A 0.5-kg mass is attached to a spring with spring constant 2.5
N/m. The spring experiences friction, which acts as a force
opposite and proportional to the velocity, with magnitude 2 N for
every m/s of velocity. The spring is stretched 1 meter and then
released.
(a) Find a formula for the position of the mass as a function of
time.
(b) How much time does it take the mass to complete one
oscillation (to pass the equilibrium point, bounce...
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