Looking For A Real Spring

Classical Mechanics Level 4

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 \(\si{\radian/\second}\).

Given your answer to 4 significant figures.

Details and Assumptions:

  • \(k = 1\ \si{\newton/\meter}\).

  • \(M = 1\ \si{\kilo\gram}\).


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