Question

**I need a solution of this structural dynamics
problem?**

**A mass with mass 1 is attached to a spring with spring
constant 64 and a dashpot giving a damping**

**16. The mass is set in motion with initial position 7
and initial velocity -10. (All values are given**

**in consistent units.) Find the position function x(t)
and plot this from t=0 to 10. What kind of**

**motion is this?**

Answer #1

Mass m=1 is attached to a spring with constant k = 4 and dashpot
constant c=2. Suppose the spring is at the equilibrium position
resting at time t=0. At t=0 the mass is struck with a hammer with
an impulse of 1. Determine the motion of the mass over time
(compute for x(t)).

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 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 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 mass weighing 16 pounds is attached to a spring and stretches
it 4 feet. You release the mass from rest
one foot below equilibrium.
(a) What is the initial value problem that models this
scenario?
(b) What is the equation of motion?
(c) What is the period of motion?
(d) Assume now that there is a damping force equivalent to 6
times the velocity. Repeat parts (a) and (b).
(e) Now assume there is still the damping force, but...

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 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...

MASS SPRING SYSTEMS problem (Differential Equations)
A mass weighing 6 pounds, attached to the end of a spring,
stretches it 6 inches.
If the weight is released from rest at a point 4 inches below
the equilibrium position, the system is immersed in a liquid that
offers a damping force numerically equal to 3 times the
instantaneous velocity, solve:
a. Deduce the differential equation that models the mass-spring
system.
b. Calculate the displacements of the mass ? (?) at all...

MASS SPRING SYSTEMS problem (Differential Equations)
A mass weighing 6 pounds, attached to the end of a spring,
stretches it 6 inches.
If the weight is released from rest at a point 4 inches below
the equilibrium position, and the entire system is immersed in a
liquid that imparts a damping force numerically equal to 3 times
the instantaneous velocity, solve:
a. Deduce the differential equation that models the mass-spring
system.
b. Calculate the displacements of the mass ? (?)...

. Write and solve a differential equation that models the motion
of a spring whose mass is 2a, spring constant b, and damping a,
where the numbers a is 3, b is 6. Assume that the initial position
is y = 1 and initial velocity is y 0 = −1. Write your solution as a
single, phase-shifted cosine function.

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