Question

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:

Answer #1

The quasi frequency is just the frequency at which the cosine
and sine functions

appearing in the formula for y(t) oscillate. So it is 2 Hz

Hence, The quasi period is 2π/2

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 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 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

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 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 small object of mass 1 kg is attached to a spring with spring
constant 2 N/m. This spring mass system is immersed in a viscous
medium with damping constant 3 N· s/m. At time t = 0, the mass is
lowered 1/2 m below its equilibrium position, and released. Show
that the mass will creep back to its equilibrium position as t
approaches infinity.

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)...

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