# Mass on a spring

## The Attempt at a Solution

any help would be appreciated!!! I keep trying and just keep getting stuck really early on.

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SteamKing
Staff Emeritus
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"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.

I don't understand where the first differential comes from

SteamKing
Staff Emeritus
Homework Helper
I don't understand where the first differential comes from
I suppose you mean Equation 1?

Do you know what ΣF = ma means?

yes force= mass*acceleration

SteamKing
Staff Emeritus
Homework Helper
yes force= mass*acceleration
And how would you apply ΣF = ma to the problem with the mass and spring?

that's where I get stuck

SteamKing
Staff Emeritus
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that's where I get stuck
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?

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

SteamKing
Staff Emeritus
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the spring is stretched so will want to go back to its original place
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?

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

SteamKing
Staff Emeritus
Homework Helper
SteamKing
Staff Emeritus
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.