## anonymous 5 years ago You have an undamped spring hanging from the ceiling with a mass of 2kg attached to the bottom. suppose the spring is stretched 1 meter by gravity. Also suppose that you stretch the spring by 1 additional meter before letting it go and afterwards apply a forcing function F(t)=2cos(3t). Write a differential equation for the spring and solve it.

1. anonymous

How do you "solve" that diff eq?

2. anonymous

$m(d ^{2}x/dt ^{2})+kx=2\cos(3t)$ and you have initial conditions x(0)=1, x'(0)=0. That should be enough to solve for position as a function of time. You can get spring constant k from the information in the problem (mg=kx) and m is given. I got the diff eq by using F=ma.

3. anonymous

Woops, forgot about initial conditions. FTW

4. anonymous

Well this is a second-order nonhomogeneous equation, where f(t) is the force function, 2cos(3t). The challenge is in finding the values of the coefficients. You can solve by the method of unknown coefficient, knowing the solution must be in the form of asint + bcost .. etc..