Understanding SHM and Finding k in a Vertical Spring Lab

[TN17]

Homework Statement

This is another question related to the vertical spring lab where we try to determine k, the spring constant.

When the vertical mass-spring system is at equilibrium, then the F in F = kx is equal to F = mg, or 9.8.

What would the F be in F = kx when the system is oscillating?
In that case, the only information we know from the experiment is x (the displacement) and mass of the object.
I'm not sure how to move on from there.

 

[rock.freak667]

Homework Statement

This is another question related to the vertical spring lab where we try to determine k, the spring constant.

When the vertical mass-spring system is at equilibrium, then the F in F = kx is equal to F = mg, or 9.8.

What would the F be in F = kx when the system is oscillating?
In that case, the only information we know from the experiment is x (the displacement) and mass of the object.
I'm not sure how to move on from there.

When the mass is initial hung, there is an initial displacement δ, so you have kδ=mg

then you displace the mass a distance 'x' such that the spring force acting is k(δ+x).

 

[TN17]

When the mass is initial hung, there is an initial displacement δ, so you have kδ=mg

then you displace the mass a distance 'x' such that the spring force acting is k(δ+x).

I understand the first part that you said because that is when it's still.
And the second part, do you mean that F = k(δ+x)? Is that when the system is oscillating?

 

[rock.freak667]

I understand the first part that you said.
And the second part, do you mean that F = k(δ+x)?

right, that F is the spring force which is just one of the forces acting when you displace the mass an additional distance x. You will still have the weight mg acting downwards.

 

[TN17]

right, that F is the spring force which is just one of the forces acting when you displace the mass an additional distance x. You will still have the weight mg acting downwards.

Okay.
But if the purpose was to find k, the spring constant, how would I do so when I only know δ and x?
That's the part I'm confused about from your equation.

 

[rock.freak667]

Okay.
But if the purpose was to find k, the spring constant, how would I do so when I only know δ and x?
That's the part I'm confused about from your equation.

If you need to get 'k' and you have 'δ', then you just need to use kδ=mg or k=mg/δ.