(adsbygoogle = window.adsbygoogle || []).push({}); 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:

[tex]\frac{1}{K_{eff}} = \frac{1}{k_{1}} + \frac{1}{k_{2}}[/tex]

2. Relevant equations

[tex]F = -kx [/tex]

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:

[tex] F1 = -k_{1} x_{1} [/tex]

[tex] F2 = -k_{2} x_{2} [/tex]

and

1)

[tex] F1 + F2 = 0 [/tex]

and a resultant force =

[tex] F_{r} = -k_{eff} x [/tex]

2)

[tex] x = x1 + x2 [/tex]

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

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# Homework Help: Question on springs

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