A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This

Chapter 2, Problem 4

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This spring-mass system is immersed in a viscous medium with damping constant 3 N.s/m. At time t = 0, the mass is lowered 1/2 m below its equilibrium position, and released. Show that the mass will creep back to its equilibrium position as t approaches infinity

Questions & Answers

QUESTION:

A small object of mass 1 kg is attached to a spring with spring constant 2N/m. This spring-mass system is immersed in a viscous medium with damping constant 3 N.s/m. At time t = 0, the mass is lowered 1/2 m below its equilibrium position, and released. Show that the mass will creep back to its equilibrium position as t approaches infinity

ANSWER:

Step 1 of 2

Let  be the position of the mass away from the equilibrium position at time .

Write the differential equation as follows.

                                                            

The initial conditions will be  and .

Write the charecteristic equation and find roots.

                                                      

The general solution will be as follows.

                                                    

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back