Question
In: Physics
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resis- tance numerically equal to the magnitude of the instanta- neous velocity. If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response.
-
(a) Find the gain function if the external force is f(t) = cos(ωt).
-
(b) Verify that the amplitude predicted by your work in (a) for an ex- ternal force f(t) = cos(3t) is consistent with the amplitude of the response you found in the body of the problem (that they do not match exactly may be attributable to the phase shift in the forcing).
Solutions
genius_generous answered 8 months agoRelated Solutions
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity. If the system is driven by
an external force of 9cos(3t)−6sin(3t) N,determine the steady-state
response in the form Rcos(ωt−δ).
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity. If the system is driven by
an external force of 15cos(3t)−10sin(3t) N,determine the
steady-state response in the form Rcos(ωt−δ)
spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is attached...
spring-mass system has a spring constant of 3 Nm. A mass of 2 kg
is attached to the spring, and the motion takes place in a viscous
fluid that offers a resistance numerically equal to the magnitude
of the instantaneous velocity. If the system is driven by an
external force of 15cos(3t)−10sin(3t) N,determine the steady-state
response in the form Rcos(ωt−δ).
R= _________
ω=__________
δ=___________
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...
A block of mass 1.59 kg is connected to a spring of spring constant 148 N/m...
A block of mass 1.59 kg is connected to a spring of spring
constant 148 N/m which is then set into oscillation on a surface
with a small coefficient of kinetic friction. The mass is pulled
back 30.6 cm to the right and released. On the first right to left
oscillation, the mass reaches 29.38 cm to the left.
Part A
What is the coefficient of friction?
Part B
To what distance does the mass return on the slide back...
a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and...
a. A 0.5 kg mass attached to a linear spring, with spring
constant 5 N/m and damping constant 0.2 kg/s, is initially
displaced 10 cm from equilibrium. (a) What is the natural frequency
of oscillation? What is its period of oscillation? How long does it
take for the amplitude to decrease to 10% of its starting value?
How many oscillations have occurred in this time? What fraction of
the initial energy remains after this time?
b. Two traveling waves with...
1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is...
1. A mass of 0.019 kg attached to a spring with spring constant
27.0 N/m is pulled to the right 8.0 cm and released. The mass
oscillates with a frequency of 6.0 Hz. If the mass is pulled to the
right 16.0 cm before being released, what is the frequency?
a. 6.0 Hz
b. 3.0 Hz
c. 1.5 Hz
d. 12 Hz
e. 24 Hz
2. A window loses power/heat energy through a pane of glass to
the cold outside....
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
A mass of 2 kg is suspended from a spring with known spring constant of 10N/m...
A mass of 2 kg is suspended from a spring with known spring
constant of 10N/m and allowed to come to rest. it is then set in
motion by giving it an initial velocity of 150 cm/sec. Find an
expression for the motion of the mass, assuming no air
resistance.
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
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