# Question on springs

1. Jan 19, 2010

### Fanta

Finding the given spring constant

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

Consider the system represented on the figure, constituted by the mass m and two springs of constant k1 and k2.
(The image is attached)
Prove that:

$$\frac{1}{K_{eff}} = \frac{1}{k_{1}} + \frac{1}{k_{2}}$$

2. Relevant equations

$$F = -kx$$

3. The attempt at a solution

I dont know where to begin. I have to consider two different displacements: One for the first spring, and one for the second.
I think, but I am not sure, that I can consider both forces are equal.
So:

$$F1 = -k_{1} x_{1}$$

$$F2 = -k_{2} x_{2}$$

and

1)

$$F1 + F2 = 0$$

and a resultant force =

$$F_{r} = -k_{eff} x$$

2)

$$x = x1 + x2$$

I tried making a system with equations 2 and 1, but I am getting nowhere. Can anyone help?

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Last edited: Jan 19, 2010
2. Jan 19, 2010

### rock.freak667

The force on both springs are equal i.e. F1=F2

Now the force on one spring is also equal to keff(x1+x2).

I think you can now find keff

3. Jan 19, 2010

### Fanta

can you explain why is that so, please?

4. Jan 19, 2010

### rock.freak667

The force on the spring should be the same throughout.

5. Jan 19, 2010

### Fanta

Like this i found it easy to do, thanks.

but isnt that the force for both springs combined?
I mean, you have the total displacement, and the Keff.

Or I can choose any of the springs, say F1 = Keff(x1+x2) ?

Last edited: Jan 19, 2010
6. Jan 19, 2010

### rock.freak667

You can choose any spring and it should work out.

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