# Homework Help: A mass inside a horizontal spring

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1. Mar 24, 2015

### tecnica

1. The problem statement, all variables and given/known data
We have a spring of length l0 tied to two vertical non moving sticks. We place a mass m at 0,45l0 and let it oscillate. If we measure the period of an oscillation, we can find the angular frequency and calculate k. The question is, how can I calculate k1 and k2, the constants of each one of the pieces on both sides of the mass?

2. Relevant equations
w=sqrt (k/m)

3. The attempt at a solution
So the thing is, I don't know if k=k1+k2 or 1/k=1/k1+1/k2

2. Mar 24, 2015

### Orodruin

Staff Emeritus
Which one do you think is correct and why?
We require students to make attempts, the reason for this is that it helps you better in the long run if we help you think rather than simply provide you with an answer.

3. Mar 24, 2015

### tecnica

I guess it is k=k1+k2, because when you move it Δx, the force acting on it is -(k1+k2)Δx, right?

4. Mar 24, 2015

### Orodruin

Staff Emeritus
Each of the parts of the spring give a force proportional to their spring constants so what you have given is the spring constant relevant for computing the angular frequency. But you should stop and think for a moment if this is actually the spring constant k of the full spring.

5. Mar 24, 2015

### tecnica

@Orodruin So the spring constant relevant for computing the angular frequency is the one that obeys k=k1+k2, and the spring constant of the full spring obeys 1/k=1/k1+1/k2, right?

6. Mar 24, 2015

### Orodruin

Staff Emeritus
Yes. In order to solve this you will also need to think about an additional condition for the relationship between k1 and k2 (a hint is that it will depend on where the mass was connected onto the spring). I also suggest calling the spring constant of the original spring k0 and the spring constant relevant for the angular frequency k in order not to mix them up.

7. Mar 24, 2015

### Staff: Mentor

tecnica,

If you have two identical springs, except that one spring is twice as long as the other, which one exhibits a higher spring constant?

Chet

8. Mar 24, 2015

### tecnica

I'm guessing the shorter one has a higher spring constant.

Could it be l1k1+l2k2=l0k (where this k is the one used for the angular frequency)? l1 is the distance between the left vertical stick and the mass, and l2 is the distance between the mass and the right stick.

9. Mar 24, 2015

### haruspex

It might help if you concentrate on one side, l1 say. How does k1 relate to k?

10. Mar 24, 2015

### tecnica

Could it be (l1/l0)k1=k ?

11. Mar 24, 2015

### haruspex

Yes.

12. Mar 24, 2015

### Orodruin

Staff Emeritus
Yes, but with k0, the spring constant of the full spring, not k, the spring constant appearing in the angular frequency.

13. Mar 24, 2015

### haruspex

Glad you caught that - I hadn't checked back with the OP to see exactly what k meant here.

14. Mar 24, 2015

### Orodruin

Staff Emeritus
Well, part of the problem was that it was not defined in the OP but the same symbol k was used for both ... I defined it in post #6.

15. Mar 24, 2015

### tecnica

Thank you guys, I understand it all now