Question

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) Write the solution in the form x = rsen(ωt + θ). (e) What are the amplitude, frequency and period of movement?

Answer #1

A force of 720 newtons stretches a spring 4 meters. A mass of 5
kg is attached to the end of the spring and is released from a
position .5 meters below the equilibrium position with a downward
velocity of 8 meters per second. What is the equation of
motion?
Please solve using Differential equations

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...

This question is for my differential equations class so please
use differential equations to solve the problem.
A mass of 4 kg is attached to a spring hanging from a ceiling,
thereby stretching the spring 9.8 cm on coming to rest at
equilibrium. The mass is then lifted up 10 cm above the equilibrium
point and given a downward velocity of 1 m/sec. Determine the
equation of motion of the mass.

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 ? (?)...

DIFFERENTIAL EQUATIONS: An object stretches a spring 5 cm in
equilibrium. It is initially displaced 10 cm above equilibrium and
given an upward velocity of .25 m/s. Find and graph its
displacement for t > 0. Find the frequency, period, amplitude,
and phase angle of the motion.

. 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.

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...

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...

Solve the following differential equations.
A spring has a constant of 4 N/m. The spring is hooked a mass of
2 kg. Movement takes place in a viscous medium that opposes
resistance equivalent to instantaneous speed. If the system is
subjected to an external force of (4 cos(2t) - 2 sin(2t)) N.
Determine:
a. The position function relative to time in the transient state
or homogeneous solution
b. Position function relative to time in steady state or
particular solution
c....

3. A mass of 5 kg stretches a spring 10 cm. The mass is acted on
by an external force of 10 sin(t/2) N (newtons) and moves in a
medium that imparts a viscous force of 2 N when the speed of the
mass is 4 cm/s. If the mass is set in motion from its equilibrium
position with an initial velocity of 3 cm/s, formulate the initial
value problem describing the motion of the mass. Then (a) Find the...

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