# Help finding equation of motion

## Homework Statement

A 1/4kg mass is attached to spring with stiffness of 4N/m. The damping constant for the system is 1 N-sec/m. If the mass is displaced 1/2 meter up and given an initial velocity of 1 m/sec upward, find the equation of motion. What is the maximum displacement that the mass will attain??

I don't know how to get started with this. I know the spring equation Fs=-kx. So, Fs would just equal 1 N Kg/m. I just don't know what to do. Any help would be appreciated.

## Answers and Replies

Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
Since you posted this in Introductory Physics I assume you aren't familiar with differential equations. In that case you would have to have been taught the equation of motion for a damped oscillator. Is that the case? Are there any equations that your teacher has presented on this?

I have the equation: (m)y(doubleprime(t)) + gamma(y prime(t)) + ky(t)=0

m = .25kg/(9.81 m/second^2)
gamma = 1N-s/m k=4N/m

so, the equation of motion is:

0.025y(doubleprime) + y(prime) + 4y=0

And for an equation of that type, do you know how to solve for y(t)? If you have the general technique, you should be able to enter in your boundary conditions (initial speed, initial displacement) during intermediate steps to get to an expression for displacement.