What Is the Frequency of Oscillation for a Mass on a Spring?

[sharkasm]

Homework Statement

This is number 23 in ch. 15 of Halliday, Resnick, and Walker 's Fundamentals of Physics.
" A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at a rest position y_i such that the spring is at its rest length. The object is then released from y_i and oscillates up and down, with its lowest position being 10 cm below y_i. What is the frequency of the oscillation?

Homework Equations

<br /> F=-kx, \, y&#039;&#039;+\frac{k}{m}y=-g, y=Acos(\sqrt{\frac{k}{m}}+\phi)+\frac{-gm}{k}<br /> [tex\]<br /> mgh+\frac{1}{2}mv^2=\frac{1}{2}kx^2 [\tex]&lt;br /&gt; f=2\pi\omega=2\pi\sqrt{\frac{k}{m}}[\tex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; &amp;lt;h2&amp;gt;The Attempt at a Solution&amp;lt;/h2&amp;gt;&amp;lt;br /&amp;gt; I just solved the differential equation, i can&amp;amp;#039;t seem to relate that to find the frequency, unless its something simple I&amp;amp;#039;ve overlooked. It seems like I don&amp;amp;#039;t have enough information to solve it...

 

[ehild]

Homework Equations

<br /> F=-kx, \, y&#039;&#039;+\frac{k}{m}y=-g, y=Acos(\sqrt{\frac{k}{m}}+\phi)+\frac{-gm}{k}<br /> [tex\]<br /> mgh+\frac{1}{2}mv^2=\frac{1}{2}kx^2 [\tex]&lt;br /&gt; f=2\pi\omega=2\pi\sqrt{\frac{k}{m}}[\tex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; &amp;lt;h2&amp;gt;The Attempt at a Solution&amp;lt;/h2&amp;gt;&amp;lt;br /&amp;gt; I just solved the differential equation, i can&amp;amp;#039;t seem to relate that to find the frequency, unless its something simple I&amp;amp;#039;ve overlooked. It seems like I don&amp;amp;#039;t have enough information to solve it...

&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; Check the equations, if you copied them correctly. &amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; What is the meaning of f in the third equation? &amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; ehild

 

[sharkasm]

i forget a t next to \sqrt{\frac{k}{m}}[\tex] in the solution for y<br /> f is the frequency of the oscillator

 

[ehild]

The equation for the frequency is also wrong. Check it.

Neither the spring constant nor the mass of the object was given. But you should know that the object oscillates around the equilibrium position where it would stay if you released it very slowly. At this equilibrium position the resultant force on the object is zero. Write this condition, and you find k/m. ehild