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## Main Question or Discussion Point

My textbook derived an expression for the frequency of oscillation of a mass m attached horizontally to a spring with mass M and constant k. Assuming that M<<m, it got that

[tex]\omega^2 = \frac{k}{m + M/3}[/tex].

The author used the conservation of energy to get this expression, but he assumed that the total potential energy still still satisfies [tex]U = \frac{1}{2} k x^2[/tex], where x is the extension of the spring. Why is this formula still correct?

Also, I wanted to derive the same result using forces, but I'm having some trouble. How would I go about this? Thanks a lot!

[tex]\omega^2 = \frac{k}{m + M/3}[/tex].

The author used the conservation of energy to get this expression, but he assumed that the total potential energy still still satisfies [tex]U = \frac{1}{2} k x^2[/tex], where x is the extension of the spring. Why is this formula still correct?

Also, I wanted to derive the same result using forces, but I'm having some trouble. How would I go about this? Thanks a lot!