Question

. 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.

Answer #1

A particular spring has a spring constant of 50 Newton/meters.
Suppose a 1/2 kg mass is hung on the spring and is initially sent
in motion with an upward velocity of 10 meters per second, 1/2
meter below the equilibrium position.
A) Write down the DE that models the motion of this spring.
B) Write down the initial conditions.
C) Find the equation of motion for the spring.
D) Suppose this spring mass system experiences a viscous damping
term that...

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 ? (?)...

.1.) Modelling using second order differential equations
a) Find the ODE that models of the motion of the dumped spring
mass system with mass m=1, damping coefficient c=3, and spring
constant k=25/4 under the influence of an external force F(t) = cos
(2t).
b) Find the solution of the initial value problem with x(0)=6,
x'(0)=0.
c) Sketch the graph of the long term displacement of the mass
m.

DIFFERENTIAL EQUATIONS
1. A force of 400 newtons stretches a spring 2 meters. A mass of
50 kilograms is attached to the end of the
spring and is initially released from the equilibrium position with
an upward velocity of 10 m/s. Find the equation of
motion.
2. A 4-foot spring measures 8 feet long after a mass weighing 8
pounds is attached to it. The medium through
which the mass moves offers a damping force numerically equal to
times the...

Suppose the motion of a weight attached to a spring is given by
the differential equation
y′′+ 6y+ 10y= 0
and
y(0) = 0, y′(0) = 3. Find the solution y(t) to this initial
value problem.

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

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.

Applications of higher order differential equations
A spring has one of its ends fixed, and a force of 15 N
stretches it 20cm. A mass of 4 Kg is attached to the end of the
spring, and the system is set in motion with initial position = 60
cm and initial velocity = 1.5 m/s.
(a) Find the spring constant.
(b) Write a problem of initial conditions for spring stretching, in meters.
(c) Solve the problem posed in (b).
(d)...

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?

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