A 10 kg mass attached to a spring stretches the spring 2 m beyond its natural...
A 10 kg mass attached to a spring stretches the spring 2 m
beyond its natural length. At
time t = 0, an external force of f (t ) = 20cos 4t Newtons is
applied to the system, and the
system is damped by a force of 3 N per m/s of motion. Assuming an
initial position at
equilibrium and no initial velocity, find the equation of motion
and the phase angle.
You can use decimals here if you hate ugly fractions … (thousandths
place). However, by
doing so your are admitting you are a lesser being, not worthy of
being a mathematics
major (ie, engineering, physics, etc).
Homework Answers
Add Answer to:
A 10 kg mass attached to a spring stretches the spring 2 m
beyond its natural...
1) A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg...
1) A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offer a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of 0.2m/sec a) Find the equation for the position if the system is exerted by an external force of f(t) = 4 cost. b)...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
Differential Equation problem We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed t...
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass...
A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass is released from its equilibrium position with a downward velocity of 1 m/s. Air resistance adds a damping force equal to one fifth of the velocity of the mass. Set up an initial value problem for the position x(t) of the mass at time t. Determine whether the system is overdamped, underdamped or critically damped. You can assume the acceleration of gravity g equals...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 8 m. The mass is in a medium that exerts a viscous resistance of 576 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 18 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7= c) If the initial value...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value...
Q4. A mass of 1 slug, when attached to a spring, stretches it 2 feet and...
Q4. A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting att 0, an external force equal to f(t) is applied to the system. Given that the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity, solve the resulting initial value problem when (a) f(t) 0 (b) s) e sin 4t. Also determine the limit lim r()
A 1 kg object is attached to a spring and stretches it 0.2 m on its...
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
Suppose a mass of 1 kg is attached to a spring with spring constant k =...
Suppose a mass of 1 kg is attached to a spring with spring constant k = 2, and rests at equilibrium position. Starting at t = 0, an external force of f(t) = e t is applied to the system. Suppose the surrounding medium offers a damping force numerically equal to β times the instantaneous velocity, where β > 0 is some given number. (a) What is the IVP governing this harmonic motion. (b) For what value(s) of β will...
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is...
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is removed and replaced with a mass weighing 51.2 pounds, which is initially released from a point 4 inches above the equilibrium position with an downward velocity of ft/s. Find the equation of motion, ä(t). (g = 32 ft/s2) (7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that...
1) A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offer a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of 0.2m/sec a) Find the equation for the position if the system is exerted by an external force of f(t) = 4 cost. b)...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 8 m. The mass is in a medium that exerts a viscous resistance of 576 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 18 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7= c) If the initial value...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value...
Q4. A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting att 0, an external force equal to f(t) is applied to the system. Given that the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity, solve the resulting initial value problem when (a) f(t) 0 (b) s) e sin 4t. Also determine the limit lim r()
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is removed and replaced with a mass weighing 51.2 pounds, which is initially released from a point 4 inches above the equilibrium position with an downward velocity of ft/s. Find the equation of motion, ä(t). (g = 32 ft/s2) (7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that...
Most questions answered within 3 hours.
-
Project management question:
Name 3 different types of resources (hint: humans are one
type)
asked 1 minute from now -
Consider the following reaction: C 2H 2( g) + 2H 2( g) C 2H 6(
g)...
asked 6 minutes ago -
Consider a 1.0 L buffer containing 0.092 mol L-1 HCOOH and 0.100
mol L-1 HCOO-. What...
asked 15 minutes ago -
Koch Realty has owned a vacant land with a FMV of
$775,000 and an adjusted basis...
asked 20 minutes ago -
It is estimated 29% of all adults in United States invest in
stocks and that 85%...
asked 20 minutes ago -
What does a 2-sided p value of 0.04 mean? (I am not asking if it
is...
asked 34 minutes ago -
A parallel-plate capacitor is made from two aluminum-foil
sheets, each 7.8 cmcm wide and 5.1 mmlong....
asked 35 minutes ago -
1. why is toluene a stronger nucleophile than benzene?
2.why is phenol a stronger nucleophile than...
asked 52 minutes ago -
4. How can you solve for the density of the liquid from the
slope? Please show...
asked 52 minutes ago -
when 2053 j of heat is added to 46.3 g of hexane C6H14 the
temperature increases...
asked 1 hour ago -
I need new and unique answers, please. (Use your own words,
don't copy and paste), Please...
asked 1 hour ago -
MCL 445.111 et seq. deals with Home Solicitation Sales.
MCL stands for Michigan Compiled Laws which...
asked 1 hour ago