Question

A 4kg mass is attached to a spring with stiffness 80 N/m. The damping constant for the system is 16sqrt(5) N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that is will attain?

The maximum displacement is [ ] meters.

Type an exact answer, using radicals as needed

Answer #1

A 5-kg mass is attached to a spring with stiffness 225 N/m. The
damping constant for the system is 30√5 N-sec/m. If the
mass is pulled 20 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?
(Type an exact answer, using radicals as needed.)

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?

A 1/4-kg mass is attached to a spring with stiffness 52 N/m.
The damping constant for the system is 6 N-sec/m. If the mass is
moved 3/4 m to the left of equilibrium and given an initial
rightward velocity of 1 m/sec, determine the
equation of motion of the mass y(t) =
and give
its damping factor,
quasiperiod, and
quasifrequency.

A 2kg mass is attached to a spring with stiffness k = 8π2N/m.
The mass is displaced 1m to the right of the equilibrium and given
a velocity of 2π m/sec to the right. No damping and no external for
are assumed.
(a) Find the period and the frequency of the motion (with
appropriate units).
(b) Write the displacement y(t) of the mass in phase-amplitude
form (every computation must be shown).
(c) What is the maximum displacement from the equilibrium...

A 1/2 kg mass is attached to a spring with 20 N/m. The
damping constant for the system is 6 N-sec/m. If the mass is moved
12/5 m to the left of equilibrium and given an initial rightward
velocity of 62/5 m/sec, determine the equation of motion of the
mass and give its damping factor, quasiperiod, and
quasifrequency.
What is the equation of motion?
y(t)=
The damping factor is:
The quasiperiod is:
The quasifrequency is:

A spring-mass-dashpot system has a mass of 1 kg and its damping
constant is 0.2 N−Sec m . This mass can stretch the spring (without
the dashpot) 9.8 cm. If the mass is pushed downward from its
equilibrium position with a velocity of 1 m/sec, when will it
attain its maximum displacement below its equilibrium?

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 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)...

An object with mass 2.5 kg is attached to a spring with spring
stiffness constant k = 270 N/m and is executing simple harmonic
motion. When the object is 0.020 m from its equilibrium position,
it is moving with a speed of 0.55 m/s.
(a) Calculate the amplitude of the motion. ____m
(b) Calculate the maximum velocity attained by the object.
[Hint: Use conservation of energy.] ____m/s

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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