# Looking For A Real Spring

Suppose we have a spring of length $$L$$ and spring constant $$k$$. Unlike your typical massless spring, ours is real and has uniform mass density given by $$\sigma = M/L$$.

We fix one end of the spring to a table, compress it, and release it, so that it starts vibrating. Find its frequency of oscillation in $$\si{\radian/\second}$$.

Details and Assumptions:

• $$k = 1\ \si{\newton/\meter}$$.

• $$M = 1\ \si{\kilo\gram}$$.

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