Physics Problem

[Sidoh]

This is a seemingly easy problem.  I suspect I'm either fucking up something royally and overlooking some fundamental issue or the software used for homework is messed up somewhere.  Anyway, here's the problem.

You place a spring with negligible mass and a spring constant of vertically with one end on the floor.  You then drop a book with a mass of 1.20 kg onto it from a height of 0.500m above the top of the spring.  Find the maximum distance the spring will be compressed.

This is obviously a simple conservation of energy problem, but it keeps saying I'm wrong!  I'm using this relationship: , so the distance, according to this relationship, should be , which yields , but I'm clearly wrong! :(

Anyone have ideas?

[Rule]

If you placed the book on the spring from a height of 0m, the spring would clearly compress, and your formula says it would not. 

Try mg/k + sqrt(2mgh/k)

Edit:
To find the position of the object at all times, solve the differential equation:
-md²y/dt² +  ky - mg = 0
With the initial condition y(0) = 0
                                 v(0) = -sqrt(2gh)

(Guess e^(rt) as a solution, and use Euler's theorem)

[Sidoh]

Aha!

Ugh, I should have thought of that.

Thanks, Rule. :)

[Nate]

its right...8.85cm?  Atleast the answer sounds right.

[Sidoh]

its right...8.85cm?  Atleast the answer sounds right.

Rule answered the question:

If you placed the book on the spring from a height of 0m, the spring would clearly compress, and your formula says it would not. 

[Nate]

Thats cause you are treating height of the spring as 0, when its height of the spring.

[Sidoh]

Thats cause you are treating height of the spring as 0, when its height of the spring.

Reference frames are hardly objective. :P