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I don't really understand this equation and was wondering if someone could help.

The book says

when the restoring force is directly proportional to the displacement the oscillation is called SHM.

and this next part confuses me

the acceleration $a =d^2x/dt^2 = -kx/m$ so it makes sense since the second derivative of position is acc.

but how do they get that last expression?


marked as duplicate by Rob Jeffries, ACuriousMind, Kyle Kanos, garyp, BMS Nov 9 '14 at 4:43

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For an ideal spring $F_{\text{spring}} = -kx.$

When a mass attached to a spring moves horizontaly, then:

$$F_{\text{total}}=F_{\text{spring}}=ma\Rightarrow -kx =ma \Rightarrow a=-\dfrac{k}{m}x.$$

  • $\begingroup$ muchas gracias!! $\endgroup$ – Petrarca Nov 8 '14 at 22:41
  • $\begingroup$ de nada. Suerte. Cualquier duda vuelves a preguntar. Sin embargo en esta comunidad debes escribir tu pregunta y además escribir lo que has intentado hacer (y decir en dónde encuentras dificultades). Generalmente a las personas de esta comunidad no les agrada responder preguntas relacionadas con tareas (a mi sí me gusta). Sin embargo evita hacer preguntas simples porque te pueden cerrar tus preguntas. $\endgroup$ – Vladimir Vargas Nov 8 '14 at 22:54

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