Question

This question is for my differential equations class so please use differential equations to solve the...

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.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

So equation is

Characteristic equation is

is general solution

(in meters) and

Therefore, the required equation of motion is

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
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...
Applications of higher order differential equations A spring has one of its ends fixed, and a...
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)...
MASS SPRING SYSTEMS problem (Differential Equations) A mass weighing 6 pounds, attached to the end of...
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 ? (?)...
A force of 720 newtons stretches a spring 4 meters. A mass of 5 kg is...
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
A mass weighing 24 pounds attached to the end of the spring and stretches it 4...
A mass weighing 24 pounds attached to the end of the spring and stretches it 4 inches. The mass is initially released from rest from a point 3 inches above the equilibrium position with a downward velocity of 2 ft/sec. Find the equation of the motion?  
A mass weighing 19.6 N stretches a spring 9.8 cm. The mass is initially released from...
A mass weighing 19.6 N stretches a spring 9.8 cm. The mass is initially released from a point 2/3 meter above the equilibrium position with a downward velocity of 5 m/sec. (a) Find the equation of motion. (b)Assume that the entire spring-mass system is submerged in a liquid that imparts a damping force numerically equal to β (β > 0) times the instantaneous velocity. Determine the value of β so that the subsequent motion is overdamped.
Question posed after chapter 4.5 of differential equations class, book by p. blanchard, 4th edition :...
Question posed after chapter 4.5 of differential equations class, book by p. blanchard, 4th edition : Suppose we have a cube made of a light substance floating in water. Gravity always pulls the cube downward. The cube floats at an equilibrium level at which the mass of the water displaced equals the mass of the cube. If the cube is higher or lower than the equilibrium level, then there is a restoring force proportional to the size of the displacement....
DIFFERENTIAL EQUATIONS 1. A force of 400 newtons stretches a spring 2 meters. A mass of...
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 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring...
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t=0, the resulting mass-spring system is disturbed from its rest state by the force F(t)=150cos(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k= Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest...
A horizontal spring attached to a wall has a force constant of 760 N/m. A block...
A horizontal spring attached to a wall has a force constant of 760 N/m. A block of mass 1.30 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (c) Find the energy stored in the spring when the mass is stretched 5.80 cm from equilibrium and again when the mass...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT