# Mass on a spring

1. Aug 6, 2015

### Katy96

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
any help would be appreciated!!! I keep trying and just keep getting stuck really early on.

2. Aug 6, 2015

### SteamKing

Staff Emeritus
"getting stuck really early on" does not provide sufficient information to help you.

Please show what work you've done on this problem, or tell us what you don't understand about the question.

3. Aug 6, 2015

### Katy96

I don't understand where the first differential comes from

4. Aug 6, 2015

### SteamKing

Staff Emeritus
I suppose you mean Equation 1?

Do you know what ΣF = ma means?

5. Aug 6, 2015

### Katy96

yes force= mass*acceleration

6. Aug 6, 2015

### SteamKing

Staff Emeritus
And how would you apply ΣF = ma to the problem with the mass and spring?

7. Aug 6, 2015

### Katy96

that's where I get stuck

8. Aug 6, 2015

### SteamKing

Staff Emeritus
Well, what forces are acting on the mass? If you assume the mass is at rest at point O, and you move it x-distance to the right, what happens to the spring? What does the displacement of the spring do to the mass?

9. Aug 6, 2015

### Katy96

the spring is stretched so will want to go back to its original place

10. Aug 6, 2015

### SteamKing

Staff Emeritus
Yes, but what does the tendency of the spring to unstretch itself do to the mass? What does it take to stretch the spring in the first place?

11. Aug 6, 2015

### Katy96

it has to be stretched by something and to go back to its original it passes and oscillates

12. Aug 6, 2015

### SteamKing

Staff Emeritus
13. Aug 6, 2015

### Katy96

14. Aug 6, 2015

### SteamKing

Staff Emeritus
In your problem, you move the mass a distance x. What does that create in the spring? Make the mass a free body and label all the forces acting on it.

15. Aug 6, 2015

### TomW17

First thing's first: you need to draw a good free body diagram. Label all the forces acting on the mass and their directions. The sum of these forces will be equal to the mass * the acceleration of the body (remember $a(t) = \ddot{x}(t)$) , and the required DE will fall out pretty quickly from this.