Question
In: Advanced Math
A spring with a spring constant 4 N/m is loaded with a 2 kgmass and allowed...
A spring with a spring constant 4 N/m is loaded with a 2 kgmass and allowed to reach equilibrium. It is then displaced 1 meter downward and released. Suppose the mass experiences a damping force in Newtons equal to 1 times the velocity at every point and an external force of F(t)=4sin(3t) driving the system. Set up a differential equation that describes this system and find a particular solution to this non-homogeneous differential equation:
Solutions
Expert Solution
spring constant 
mass 
damping force in Newtons equal to 1 times the velocity
so damping constant is 
external force is 
.
DE is given by
....................differential
equation for this system
.
in question mention that, find an only a particular solution
.
here we have 
so assume that particular solution is
....................(1)
.
put all values in DE
.
.
.
compare coefficient both sides
....................put
both constants in equation 1
.
......................
particular solution
Colby Messinger answered 2 years agoRelated Solutions
A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...
A mass weighing 4 N is attached to a spring whose constant is 2
N/m. The medium offers a damping force that is numerically equal to
the instantaneous velocity. The mass is initially released from a
point 1 m above the equilibrium position with a downward velocity
of 6 m/s. Determine the time at which the mass passes through the
equilibrium position. (Use
g = 9.8 m/s2
for the acceleration due to gravity.)
14
s
Find the time after the...
A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...
A mass weighing 4 N is attached to a spring whose constant is 2
N/m. The medium offers a damping force that is numerically equal to
the instantaneous velocity. The mass is initially released from a
point 1 m above the equilibrium position with a downward velocity
of 6 m/s. Determine the time at which the mass passes through the
equilibrium position. (Use
g = 9.8 m/s2
for the acceleration due to gravity.)
s
Find the time after the mass...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resis- tance numerically equal to the
magnitude of the instanta- neous velocity. If the system is driven
by an external force of (12 cos 3t − 8 sin 3t) N, determine the
steady-state response.
(a) Find the gain function if the external force is f(t) =
cos(ωt).
(b)...
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and...
A mass of 2 kilogram is attached to a spring whose constant is 8
N/m, and the entire system is then submerged in a liquid that
imparts a damping force equal to 8 times the instantaneous
velocity. At t = 0 the mass is released from the equilibrium
position with no initial velocity. An external force f(t) =
2U(t−1)*e^(−2(t−1)) is applied.
(a) Write f(t), the external force, as a piecewise function and
sketch its graph.
(b) Write the initial-value problem....
A spring with a spring constant ? k of 100 pounds per foot is loaded with...
A spring with a spring constant ? k of 100 pounds per foot is
loaded with 1-pound weight and brought to equilibrium. It is then
stretched an additional 1 inch and released. Find the equation of
motion, the amplitude, and the period. Neglect friction. Then find
y(t)
A spring cannon has a spring constant of 350 N / m and the bullet weighs...
A
spring cannon has a spring constant of 350 N / m and the bullet
weighs 10 grams. What is the maximum height, measured above the
equilibrium position of the spring, that the spring cannon can
shoot the ball up to if the maximum compression of the spring is
3.0 cm?
(Continuation of the previous question)
Before firing, the spring is compressed 2.0 centimeters in
relation to the equilibrium position and the firing angle is set to
?? = 41...
A 175 g mass is connected to a light spring of force constant 2 N/m that...
A 175 g mass is connected to a light spring of force constant 2
N/m that is free to oscillate on a horizontal, frictionless track.
The mass is displaced 3 cm from the equilibrium point and released
from rest.
a.) Find the period of the motion.
Answer in units of s.
b.) What is the maximum speed of the mass? Answer in units of
m/s.
c.)
What is the maximum acceleration of the mass? Answer in units of
m/s^2 .
A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...
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...
In a spring gun system, a spring with a spring force constant 420 N/mN/m , is compressed...
In a spring gun system, a spring with a spring force constant
420 N/mN/m , is compressed 0.13 mm . When fired, 80.9 %%
of the elastic potential energy stored in the spring is eventually
converted into kinetic energy of a 6.10×10−2 kgkg
uniform ball that is rolling without slipping at the base of a
ramp. The ball continues to roll without slipping up the ramp with
89.6 %% of the kinetic energy at the bottom converted into an
increase in...
A block of mass 1.59 kg is connected to a spring of spring constant 148 N/m...
A block of mass 1.59 kg is connected to a spring of spring
constant 148 N/m which is then set into oscillation on a surface
with a small coefficient of kinetic friction. The mass is pulled
back 30.6 cm to the right and released. On the first right to left
oscillation, the mass reaches 29.38 cm to the left.
Part A
What is the coefficient of friction?
Part B
To what distance does the mass return on the slide back...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- An investor is considering purchasing a Treasury bond with a 20 year maturity, an 8% coupon...
- Write a program that copies the contents of one file to a destination file. This program...
- how to conduct a marketing mix for 3d crest white strips
- Is big data analytics used for service innovation at Amazon? If so, please write a brief...
- A shrink-fit process has been used to enhance the pressure carrying capacity of a cylinder. During...
- Ten-year zero coupon bonds issued by the U.S. Treasury have a face value of $1,000 and...
- The Blossom Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a...
ADVERTISEMENT