Why is my spring angular frequency negative when it should be positive?

[shanepitts]

Homework Statement

In image below

Homework Equations

F_s=-kx

The Attempt at a Solution

In image below

This question might be amateurish

Why does my answer equate to negative angular frequency when the given result is positive?
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[Qwertywerty]

Firstly , mg = (k₁ + k₂)x and not it's negative .

Secondly , what have you done here ?
Why have you equated mg to k_eqx ? This only gives you the equilibrium position .

Correct derivation would be - find k_eq , then write the formula for w interms of k and m .

Hope this helps .

 

[shanepitts]

Firstly , mg = (k₁ + k₂)x and not it's negative .

Secondly , what have you done here ?
Why have you equated mg to k_eqx ? This only gives you the equilibrium position .

Correct derivation would be - find k_eq , then write the formula for w interms of k and m .

Hope this helps .

Thank you, it helps. But I am wondering how do I find
k_eq?

 

[Nathanael]

Thank you, it helps. But I am wondering how do I find
k_eq?

There is a certain spring constant, k_eq, such that if we put a single spring with that spring constant in place of the other two springs, it would have the same effect.

So if you displace the mass by Δx, then the two springs exert a total force of F on the mass. That means (by the above definition) the effective spring constant is F/Δx.

So now try to find this total force F (from the springs) in terms of the given spring constants and Δx.

 

[shanepitts]

There is a certain spring constant, k_eq, such that if we put a single spring with that spring constant in place of the other two springs, it would have the same effect.

So if you displace the mass by Δx, then the two springs exert a total force of F on the mass. That means (by the above definition) the effective spring constant is F/Δx.

So now try to find this total force F (from the springs) in terms of the given spring constants and Δx.

Thank you