What is the Inclined Spring Problem?

[fluidistic]

Homework Statement

Check out the figure I made up to get the situation of the problem.
It's a body of mass $$m$$ that is at point $$a$$ and that we let go down on (due to gravity) the inclinated plane until it reaches a spring (with an elastic constant $$k$$) at point $$b$$. Before the spring get hitten by the body, it has a length $$l$$.
a)What is the minimal height (calculated from the ground) the body will reach?
b)Calculate the speed of the body just before it hits the spring at point $$b$$.
c)After having hit the spring, the body is encrusted into the spring. Write down and solve the equation of the movement of the body with respect to a coordinates system with its origin at the equilibrium point.

Homework Equations

,

The Attempt at a Solution

I worked out the equation of conservation of energy to be $$E=\frac{1}{2}mv^2+\frac{1}{2}k(x-x_{equilibrium})^2-\sin (\alpha)mgx$$ when the body has already touched the spring. But before this moment, I'm not sure about how to calculate it. Anyway, am I in the right way to solve the problem?
Well in fact I find it very hard to solve and I'm not sure about how to proceed. Can you help me to get started? (on a), of course).

 

[Hootenanny]

Homework Statement

Check out the figure I made up to get the situation of the problem.
It's a body of mass $$m$$ that is at point $$a$$ and that we let go down on (due to gravity) the inclinated plane until it reaches a spring (with an elastic constant $$k$$) at point $$b$$. Before the spring get hitten by the body, it has a length $$l$$.
a)What is the minimal height (calculated from the ground) the body will reach?
b)Calculate the speed of the body just before it hits the spring at point $$b$$.
c)After having hit the spring, the body is encrusted into the spring. Write down and solve the equation of the movement of the body with respect to a coordinates system with its origin at the equilibrium point.

Homework Equations

,

The Attempt at a Solution

I worked out the equation of conservation of energy to be $$E=\frac{1}{2}mv^2+\frac{1}{2}k(x-x_{equilibrium})^2-\sin (\alpha)mgx$$ when the body has already touched the spring. But before this moment, I'm not sure about how to calculate it. Anyway, am I in the right way to solve the problem?
Well in fact I find it very hard to solve and I'm not sure about how to proceed. Can you help me to get started? (on a), of course).

You've got the right idea with conservation of energy. What form of energy does the body have before it is released? How much energy does it have at this point?

 

[fluidistic]

Thank you Hootenanny, I could solve the problem. I only got some dificulties in encountering $$x_{\text{equilibrium}}$$. Not that much in fact but what I did was more or less formal : I assumed that it is situated at the middle point between $$x_{min}$$ and $$x_{max}$$ without justifying why it is so.
Anway, about

What form of energy does the body have before it is released? How much energy does it have at this point?

it has only potential energy since its speed is 0. The problem was a bit difficult because I had to establish twice the laws of energy. One before the body hit the spring and the other when it is encastred into the spring. And also convert distances in function of $$\alpha$$, but I could do it.